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Improved Constraints on Primordial Gravitational Waves using Planck , WMAP, and BICEP/ Keck Observations through the 2018 Observing Season
Open accessAbstract
We present results from an analysis of all data taken by the BICEP2, Keck Array, and BICEP3 CMB polarization experiments up to and including the 2018 observing season. We add additional Keck Array observations at 220 GHz and BICEP3 observations at 95 GHz to the previous 95/150/220 GHz dataset. The Q/U maps now reach depths of 2.8, 2.8, and 8.8 μK_{CMB} arcmin at 95, 150, and 220 GHz, respectively, over an effective area of ≈600 square degrees at 95 GHz and ≈400 square degrees at 150 and 220 GHz. The 220 GHz maps now achieve a signal-to-noise ratio on polarized dust emission exceeding that of Planck at 353 GHz. We take auto- and cross-spectra between these maps and publicly available WMAP and Planck maps at frequencies from 23 to 353 GHz and evaluate the joint likelihood of the spectra versus a multicomponent model of lensed ΛCDM+r+dust+synchrotron+noise. The foreground model has seven parameters, and no longer requires a prior on the frequency spectral index of the dust emission taken from measurements on other regions of the sky. This model is an adequate description of the data at the current noise levels. The likelihood analysis yields the constraint r_{0.05}<0.036 at 95% confidence. Running maximum likelihood search on simulations we obtain unbiased results and find that σ(r)=0.009. These are the strongest constraints to date on primordial gravitational waves.
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TL;DR
The BICEP/Keck collaboration analyzed all BICEP2, Keck Array, and BICEP3 CMB polarization data through the 2018 observing season, combined with WMAP and Planck maps, to constrain primordial gravitational waves. They report the strongest limit to date, \(r_{0.05}<0.036\) at 95% confidence, with no significant evidence for \(r>0\).
Key findings
- The baseline likelihood gives \(r_{0.05}=0.014^{+0.010}_{-0.011}\) and \(r_{0.05}<0.036\) at 95% confidence; simulations give \(\sigma(r)=0.009\) and a median 95% upper limit of \(r_{0.05}<0.019\).
- Foreground parameters: \(A_{d,353}=4.4^{+0.8}_{-0.7}\,\mu\mathrm{K}^2\), \(A_{\mathrm{sync},23}<1.4\,\mu\mathrm{K}^2\) at 95% confidence, and \(\beta_d=1.49^{+0.13}_{-0.12}\); the synchrotron amplitude now peaks at zero.
- New maps reach depths of 2.8, 2.8, and 8.8 \(\mu\mathrm{K}_{\mathrm{cmb}}\,\mathrm{arcmin}\) at 95, 150, and 220 GHz over effective areas of \(\approx 600\) square degrees at 95 GHz and \(\approx 400\) square degrees at 150 and 220 GHz.
- The 220 GHz maps achieve signal-to-noise on polarized dust emission exceeding that of Planck at 353 GHz; the maximum-likelihood model has PTE 0.94, and the previous limits improved from \(r_{0.05}<0.12\) (BKP) to \(<0.09\) (BK14) to \(<0.07\) (BK15) to \(<0.036\) (BK18).
Methods
- Analysis of BICEP2, Keck Array, and BICEP3 CMB polarization data through the 2018 observing season, adding Keck 220 GHz and BICEP3 95 GHz data to the previous 95/150/220 GHz dataset; maps are made into Q/U, purified to B-modes, apodized, Fourier transformed, and used to form auto- and cross-spectra.
- Joint likelihood uses 66 BB auto- and cross-spectra between BICEP/Keck maps and WMAP 23/33 GHz plus Planck 30, 44, 143, 217, and 353 GHz maps, over \(20<\ell<330\) with 9 bandpowers per spectrum.
- The model is lensed \(\Lambda\)CDM + \(r\) + dust + synchrotron + noise with eight parameters, evaluated with Hamimeche-Lewis likelihood and CosmoMC MCMC; the dust frequency spectral index prior is removed, and the bandpower covariance matrix comes from 499 signal-and-noise simulations.
Limitations
- The paper states that dust decorrelation and foreground complexity more generally “will remain a serious concern” as sensitivity improves, and that the sample variance of the lensing component already dominates \(\sigma(r)\).
- The paper states that the baseline does not allow the dust decorrelation parameter \(\Delta_d\) to vary freely because it is biasing with respect to \(r\); it also notes that including EE spectra assumes an exact EE/BB ratio of 2 and “should not be overinterpreted.”
- The paper states residual uncertainties from point-source polarized flux may yield an upward bias on \(r\) of \(1-3\times10^{-3}\), and noise-bias imperfections may yield a downward bias of \(2\times10^{-3}\); these are subdominant to the statistical uncertainty.
- Evident from the text: the analysis fixes the tensor spectral index \(n_t=0\), assumes a power-law dust spatial spectrum and Gaussian dust fluctuations, and relies on external WMAP/Planck data for foreground separation.
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89 Own result · 32 Sources not found · 16 Own method · 10 No basis given · 8 Own interpretation
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In the paper
“The BK18 result described in this letter, r 0 . 05 < 0 . 036, represents a fractional improvement equivalent to the two previous steps combined.”
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“This model is an adequate description of the data at the current noise levels.”
- Also stated in: § BICEP / Keck XIII: Improved Constraints on Primordial Gravitational Waves using Planck , WMAP, and BICEP/ Keck Observations through the 2018 Observing Season · p. 4 · plain
“This model is an acceptable fit to the data with the probability to exceed (PTE) the observed value of χ 2 being 0.94.”
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- The authors state this as an assumption: The synchrotron frequency spectrum is a simple power law A_sync ∝ ν^β_s.
- The authors state this as an assumption: The dust spatial power spectrum is a power law D_ℓ ∝ ℓ^α_d.
- The authors state this as an assumption: The synchrotron spatial power spectrum is a power law D_ℓ ∝ ℓ^α_s.
- Also stated in: § BICEP / Keck XIII: Improved Constraints on Primordial Gravitational Waves using Planck , WMAP, and BICEP/ Keck Observations through the 2018 Observing Season · p. 4 · plain
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In the paper
“The 220GHz maps now achieve a signal-to-noise on polarized dust emission exceeding that of Planck at 353 GHz.”
- Also stated in: § BICEP / Keck XIII: Improved Constraints on Primordial Gravitational Waves using Planck , WMAP, and BICEP/ Keck Observations through the 2018 Observing Season · p. 6 · plain
“The signal-to-noise on polarized dust emission of our 220 GHz band is now considerably higher than that of the Planck 353 GHz band-i.e. the 220 × 220 noise point is much further below the dust band than the P353 × P353 point.”
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- Also stated in: § BICEP / Keck XIII: Improved Constraints on Primordial Gravitational Waves using Planck , WMAP, and BICEP/ Keck Observations through the 2018 Observing Season · p. 6 · plain
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“For r , the zero-to-peak likelihood ratio is 0.46.”
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“The likelihood analysis yields the constraint r 0 . 05 < 0 . 036 at 95% confidence.”
- Also stated in: § BICEP / Keck XIII: Improved Constraints on Primordial Gravitational Waves using Planck , WMAP, and BICEP/ Keck Observations through the 2018 Observing Season · p. 1 · plain
“r 0 . 05 < 0 . 036 at 95% confidence”
- Also stated in: § ACKNOWLEDGMENTS · p. 7 · plain
“The upper limit on the tensor-to-scalar ratio tightens to r 0 . 05 < 0 . 036 at 95% confidence.”
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- Also stated in: § BICEP / Keck XIII: Improved Constraints on Primordial Gravitational Waves using Planck , WMAP, and BICEP/ Keck Observations through the 2018 Observing Season · p. 1 · plain
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“r 0 . 05 = 0 . 014 +0 . 010 -0 . 011 ( r 0 . 05 < 0 . 036 at 95% confidence)”
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“A sync , 23 < 1 . 4 µ K 2 at 95% confidence”
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“and that the data do not prefer allowing decorrelation of the dust pattern in the model.”
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“The maximum likelihood model has parameters r 0 . 05 = 0 . 011, A d , 353 = 4 . 4 µ K 2 , A sync , 23 = 0 . 6 µ K 2 , β d = 1 . 5, β s = -3 . 0, α d = -0 . 66, α s = 0 . 00, and ϵ = -0 . 11.”
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- The authors state this as an assumption: The synchrotron frequency spectrum is a simple power law A_sync ∝ ν^β_s.
- The authors state this as an assumption: The dust spatial power spectrum is a power law D_ℓ ∝ ℓ^α_d.
- The authors state this as an assumption: The synchrotron spatial power spectrum is a power law D_ℓ ∝ ℓ^α_s.
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“Running without foreground parameters on simulations which contain neither lensing or dust gives σ ( r 0 . 05 ) = 0 . 002.”
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- Probably not a substantial claim. 34
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“Running maximum likelihood search on simulations we obtain unbiased results and find that σ ( r ) = 0 . 009.”
- Also stated in: § BICEP / Keck XIII: Improved Constraints on Primordial Gravitational Waves using Planck , WMAP, and BICEP/ Keck Observations through the 2018 Observing Season · p. 5 · plain
“The distributions of maximum likelihood r values in simulations where the true value of r is zero gave σ ( r 0 . 05 ) = 0 . 020 for BK15 which is reduced to σ ( r 0 . 05 ) = 0 . 009 for BK18”
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- Also stated in: § BICEP / Keck XIII: Improved Constraints on Primordial Gravitational Waves using Planck , WMAP, and BICEP/ Keck Observations through the 2018 Observing Season · p. 5 · plain
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“The BK18 data shrinks the contours in the vertical ( r ) direction while the BAO data shrinks the contours in the horizontal ( n s ) direction and shifts the centroid slightly to the right.”
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“The Q/U maps now reach depths of 2.8, 2.8 and 8.8 µ K cmb arcmin at 95, 150 and 220 GHz respectively over an effective area of ≈ 600 square degrees at 95 GHz and ≈ 400 square degrees at 150 & 220GHz.”
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“We also find that the value of A d is very similar when evaluated over the larger BICEP3 sky coverage region and the smaller BICEP2 / Keck sky region.”
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“This improves the constraint on primordial gravitational waves parameterized by the tensor-to-scalar ratio r by more than a factor of two over our previous result to r 0 . 05 < 0 . 036 at 95% confidence, setting important additional limits on inflationary models.”
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“In the BK15 analysis the constraint on β d was prior dominated, but for BK18 we see that the data is able to constrain this parameter almost as well as the prior previously did.”
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“As compared to the previous BK15 analysis, the likelihood curve for r tightens considerably with the peak position shifting down slightly, and the A d curve tightens slightly.”
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“Freeing the amplitude of the lensing power we obtain A BB L = 1 . 03 +0 . 08 -0 . 09 , and the r constraint hardly changes.”
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“Interestingly the peak value selected is very close to the mean value from Planck 2018 analysis of larger regions of sky β d = 1 . 53 [24].”
What the sources say
- Not matchedcites [24]
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“In addition the A sync curve now peaks at zero-the weak evidence for synchrotron we saw in BK15 is no longer present.”
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“The 95GHz B map is approximately equal parts lensed-ΛCDM signal and noise.”
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“The increase of 1.5 for the real data is smaller than the average increase in the simulations indicating no evidence that synchrotron is present.”
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“With a uniform prior on A BB L (and marginalizing over all other parameters) we obtain A BB L = 1 . 03 +0 . 08 -0 . 09 showing no tension with ΛCDM.”
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“The r constraint hardly changes due to the fact that the lensing amplitude prefered by the BK18 data is very close to that predicted by the Planck 2018 cosmological parameters.”
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“In Fig. 17 switching to the updated Planck 2018 spectrum corresponds to the transition from red to black-the r constraint shifts slightly up indicating that this is a marginally relevant change at BK18 sensitivity levels.”
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- The authors state this as an assumption: The power spectrum of the polarized dust emission in the BICEP/Keck field follows a power law.
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“Due to the larger instantaneous field of view BICEP3 naturally maps a larger area of sky.”
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“Removing synchrotron from the fit (i.e. fixing As = 0, β s = 0, α s = 0 and ϵ = 0) corresponds to a nominal reduction in the number of fit parameters of 4, but the increase in the mean -2 log( L ) for the simulations (which contain no synchrotron) suggests only 2.5 effective free parameters.”
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“For the 9 × 66 = 594 bandpowers shown in Fig. 15, χ 2 = ( d -m ) T C -1 ( d -m ) = 541 . 6, where d are the bandpower values, m are the model expectation values, and C is the bandpower covariance matrix for the maximum likelihood model. This has a PTE versus the simulations of 0 . 94.”
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“The effects are similar to those seen in BK15-the r peak position shifts up, the A d curve narrows, and the A sync curve peaks strongly away from zero.”
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“The χ 2 and χ jackknife statistics do not actually have the nominal theory distributions since they are summations of bandpower values which are themselves χ 2 rather than Gaussian distributed.”
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“However, at 220 GHz we start to see dust contamination become comparable in amplitude to the ΛCDM E -modes at the edges of the field.”
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“Interestingly the peak position of A d only shifts a very small amount under these variations showing no evidence for variation of the polarized dust amplitude as averaged across the BICEP3 coverage pattern versus the subset BICEP2 / Keck fi eld.”
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“In Fig. 17 dropping the β d prior corresponds to the transition from yellow to red curvesr and A sync show very little change while A d gets just slightly wider.”
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“As seen in Figures 8 and 9 the BICEP3 sky coverage is larger than the BICEP2 / Keck region.”
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“If instead we take the sum of the normalized deviations χ = ∑ (( d -m ) /e ) where e is the square-root of the diagonal of C , we find that the PTE versus the simulations is 0.22.”
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“In a simple study we find this to be 2.2% within the multipole range 20 < ℓ < 500 (with a distribution close to Gaussian).”
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“The upper part of Fig. 14 compares the two BB spectra-a large improvement in sensitivity is again clear, and the BK18 220 GHz spectrum is sample variance limited out to ℓ ∼ 200.”
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Probably not a substantial claim. The paper’s conclusions may not depend on it.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“The E maps are dominated by ΛCDM signal, and hence are highly correlated across all three bands.”
plaincorrelational- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: unclear — It is unclear whether the paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“Comparing the three frequencies we see almost identical patterns in the T maps since ΛCDM signal is dominant.”
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it.
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Dropping WMAP results in A sync peaking strongly at zero whereas dropping LFI results in A sync peaking well above zero.”
boosteddirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: unclear — It is unclear whether the paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“Note that for the small field only version the A sync peak shifts above zero as it was in BK15.”
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it.
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“For Q and U the patterns are again extremely similar between 95 and 150 GHz, and dominated by the ΛCDM E -mode signal.”
plaincorrelational- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it. It may state two separate claims as one.
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“BICEP/ Keck alone (blue) constrains A sync and β d poorly with the r constraint peaking hard at zero.”
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: unclear — It is unclear whether the paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“In Appendix D above we saw that the absolute goodness-of-fit of the baseline model to the data is adequate.”
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it.
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“We next switch from the BK15 data set to the BK18 one-i.e. including the improved sensitivity at 220 GHz and the improved sensitivity and sky area at 95 GHz (magenta to yellow). This makes a substantial difference: the r constraint narrows and its peak position shifts down.”
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
- The authors state this as an assumption: The power spectrum of the polarized dust emission in the BICEP/Keck field follows a power law.
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Starting with the BK15 data set we first update the version of COSMOMC from Nov2016 to July2019 (green to magenta) which makes very little difference.”
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it.
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Using different apodizations also in principle reduces the correlations of the auto- and cross-spectra which are key to the separation of foreground and CMB signals. However, in the current case the penalty turns out to be negligible.”
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it.
In the paper
“Interestingly the peak value of β d = 1 . 50 selected by our data is close to the mean value from Planck 2018 analysis of larger regions of sky β P d = 1 . 53 ± 0 . 02 [24].”
What the sources say
- Not matchedcites [24]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it.
- Not matched
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“The two nominally 220 GHz receivers added before the 2015 season actually have passbands centered at ≈ 230 GHz, whereas the two added before the 2016 season have passbands centered at ≈ 220 GHz.”
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it. It may state two separate claims as one.
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“We see that the r constraint shifts down slightly and the A sync constraint shifts up slightly.”
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: unclear — It is unclear whether the paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Allowing decorrelation parameter ∆ d to vary freely while fixing ϵ = 0 leaves the nominal number of parameters unchanged and as expected hardly changes the mean value of -2 log( L ) for the simulations.”
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: unclear — It is unclear whether the paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“It is very interesting that dropping the 150 and 220 GHz bands does not substantially increase the width of the r constraint, although it is unsurprising that it does increase the widths of the A d and β d constraints.”
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: unclear — It is unclear whether the paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Synchrotron is tightly limited in all the multipole ranges, and not detected in any of them.”
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: unclear — It is unclear whether the paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Dropping the other HFI bands makes smaller additional changes (red to green).”
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it.
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“The shifts on dust parameters ( A d and β d ) are a few percent, and still within statistical uncertainty and upper bounds predicted using maximum likelihood searches on simulations.”
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: unclear — It is unclear whether the paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“We find that 60% of the simulations peak at zero, and 11% have a lower zero-to-peak ratio than the real data-i.e. show more evidence for r when the true value is in fact zero.”
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: unclear — It is unclear whether the paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“They have A d in our sky region which is much greater that the actual level and this modestly increases σ ( r ), although interestingly by an amount that is fractionally less than the increase seen in BK15.”
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: unclear — It is unclear whether the paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Neither of these models produces detectable bias on r .”
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: unclear — It is unclear whether the paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
In the paper
“The corresponding spectra for the Keck 95 GHz, 150 GHz and 220 GHz bands were found to be very similar to the BK15 results shown in Ref. [52].”
What the sources say
- Not matchedcites [52]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it.
- Not matched
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“The real data shows an increase almost exactly equal to that in the mean of simulations-i.e. the data is perfectly compatible with the lensed-ΛCDM expectation plus the simple 3 parameter dust model.”
boostedn = 2- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“The input values are recovered in the mean although formally there is a small bias detectable on A d .”
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: unclear — It is unclear whether the paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
None of the sources cited for this claim could be matched to a paper in Crossref, so there is nothing to check it against.
In the paper
“More significant, but still subdominant for the current analysis, are uncertainties from the contributions of polarized flux from point sources in our field, which estimates suggest may yield an upward bias on r of 1-3 × 10 -3 [9, 64, and recent internal work], and imperfections in our noise bias estimates as they interact with leakage deprojection filtering, which recent preliminary work suggests”
What the sources say
- Not matchedcites [9]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
- Not matchedcites [64]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
hedgedconditional- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: unclear — It is unclear whether the paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
- Not matched
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“The recovered bias is ∆( r ) = 1 . 5 ± 1 . 1 × 10 -3 , which is subdominant compared to our statistical uncertainty σ ( r ) = 0 . 009.”
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
In the paper
“In a joint analysis using multifrequency data from the Planck experiment it was shown that most or all of this is due to polarized emission from dust in our own galaxy [10, hereafter BKP].”
What the sources say
- Not matchedcites [10]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim.
- Not matched
None of the sources cited for this claim could be matched to a paper in Crossref, so there is nothing to check it against.
In the paper
“As part of our standard data reduction we 'deproject' leading order temperature to polarization leakage [9, 34]-in Appendix F we quantify possible residual leakage and some other possible systematics.”
What the sources say
- Not matchedcites [9]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
- Not matchedcites [34]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim.
- Not matched
In the paper
“Our BICEP/ Keck program first reported detection of an excess over the lensing B -mode expectation at 150 GHz in Ref. [9].”
What the sources say
- Not matchedcites [9]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it.
- Not matched
In the paper
“Under the ΛCDM standard model the CMB polarization pattern is mostly E -mode, with a much smaller B -mode component which arises due to gravitational deflections (lensing) of the CMB photons after their last scattering [5].”
What the sources say
- Not matchedcites [5]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
- Not matched
None of the sources cited for this claim could be matched to a paper in Crossref, so there is nothing to check it against.
In the paper
“The EE spectra were not used to derive the model but agree well with it under the assumption that EE/BB = 2 for dust, as is known to be close to the case [23, 24].”
What the sources say
- Not matchedcites [23]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
- Not matchedcites [24]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
boosted- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: unclear — It is unclear whether the paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
- The authors state this as an assumption: For dust, EE/BB = 2.
- Not matched
In the paper
“At the South Pole the atmosphere is exceptionally transparent and stable at the observation frequencies [17, Fig. 5].”
What the sources say
- Not matchedcites [17, Fig. 5]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it. It may state two separate claims as one.
- Not matched
What the paper did — it cites no source for this, so there is none to check. The quote shows it is in the paper.
In the paper
“To test for systematic contamination we carry out our usual 'jackknife' internal consistency (null) tests on the new 95GHz and 220GHz data as described in Appendices B and C.”
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it.
None of the sources cited for this claim could be matched to a paper in Crossref, so there is nothing to check it against.
In the paper
“Planck analysis consistently finds approximate power law behavior of both the EE and BB dust spectra with exponents ≈ -0 . 4 [23, 24].”
What the sources say
- Not matchedcites [23]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
- Not matchedcites [24]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
plaincorrelational- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it.
- Not matched
None of the sources cited for this claim could be matched to a paper in Crossref, so there is nothing to check it against.
In the paper
“Since primordial gravitational waves will produce E -modes and B -modes approximately equally it was realized in the late 1990's that the best way to search for them is to look for an excess B -mode signal [6-8].”
What the sources say
- Not matchedcites [6]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
- Not matchedcites [7]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
- Not matchedcites [8]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
- Not matched
In the paper
“(Using the S-PASS data [30] we estimate that the expectation is A sync , 23 ≈ 0 . 4 µ K 2 in the BICEP/ Keck fi eld, which is consistent with our A sync likelihood curve.)”
What the sources say
- Not matchedcites [30]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
hedgedcorrelational- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: unclear — It is unclear whether the paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
- Not matched
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“The φ 2 / 3 model now lies outside the 95% contour as does the band of natural inflation models.”
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
In the paper
“If we can detect or set limits on primordial gravitational waves we can set limits on these models [4], and probe physics at energy scales far higher than can ever be accessed in laboratory experiments.”
What the sources say
- Not matchedcites [4]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
- Not matched
In the paper
“This is an interesting result given the Planck 2018 TT,TE,EE+lowE result A L = 1 . 18 ± 0 . 065 [2, Eqn. 36b].”
What the sources say
- Not matchedcites [2]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it.
- Not matched
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“In addition in the right panel of Fig. 19 we see that there is very little degeneracy between r and A BB L implying that all one now needs from ΛCDM is the template shape of the lensing B -mode spectrum, and not the amplitude.”
plaincorrelational- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: unclear — It is unclear whether the paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
What the paper did — it cites no source for this, so there is none to check. The quote shows it is in the paper.
In the paper
“We note that we did not look at the non-jackknife spectra until the above data removals had been done and the null tests determined to be satisfactory.”
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it.
In the paper
“Recently Ref. [55] reported evidence for line-of-sight decorrelation in Planck data by using HI data to select sight lines which integrate over multiple dust clouds.”
What the sources say
- Not matchedcites [55]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it.
- Not matched
What the paper did — it cites no source for this, so there is none to check. The quote shows it is in the paper.
In the paper
“To keep down the total number of spectra we drop the other Planck bands since these provide a negligible amount of additional information.”
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it.
In the paper
“We note that analysis of 2.3 GHz data from S-PASS in conjunction with WMAP and Planck fi nds β s = -3 . 2 with no detected trends with galactic latitude or angular scale [30]”
What the sources say
- Not matchedcites [30]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it. It may state two separate claims as one.
- Not matched
None of the sources cited for this claim could be matched to a paper in Crossref, so there is nothing to check it against.
In the paper
“Using different apodizations suppresses the amplitude of the cross-spectra as compared to the auto-spectra but this is automatically taken into account in the bandpower window function calculations [18, 53].”
What the sources say
- Not matchedcites [18]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
- Not matchedcites [53]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: unclear — It is unclear whether the paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
- Not matched
In the paper
“This study uses maps of the effective number of clouds taken from Ref. [56] which in Sec. 4.2 specifically examines the BICEP/ Keck patch and states that 'one cloud dominates the column density in the majority of pixels in the BICEP/ Keck region'.”
What the sources say
- Not matchedcites [56]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim.
- Not matched
None of the sources cited for this claim could be matched to a paper in Crossref, so there is nothing to check it against.
In the paper
“In this section we perform tests of the new 2016, 2017 and 2018 data which are the same as those performed on the previous BICEP/ Keck data in Sec. VII.C of Ref. [9], Sec. 6.3 of Ref. [14], Appendix B of BK14, and Appendix B of BK15.”
What the sources say
- Not matchedcites [9]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
- Not matchedcites [14]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it.
- Not matched
What the paper did — it cites no source for this, so there is none to check. The quote shows it is in the paper.
In the paper
“Running maximum likelihood searches on simulations indicates that this results in σ ( r ) as low as any other option with no detectable bias on r .”
hedgeddirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: unclear — It is unclear whether the paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
In the paper
“Ref. [30] finds a value at the bottom end of this range ( ≈ -1) from the S-PASS data for BB at high galactic latitude.”
What the sources say
- Not matchedcites [30]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it.
- Not matched
What the paper did — it cites no source for this, so there is none to check. The quote shows it is in the paper.
In the paper
“For all effects considered, the magnitude of the estimated bias on r is significantly smaller than our statistical uncertainty, and not all of the biases have the same sign, which should lead to partial cancelation.”
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
What the paper did — it cites no source for this, so there is none to check. The quote shows it is in the paper.
In the paper
“In this leakage analysis for BK18, care was taken to minimize systematic contamination in the composite beam maps from the FFBM analysis pipeline itself, e.g. by minimizing non-Gaussian noise and excess smoothing.”
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Such variation of the dust amplitude across the field can potentially produce bias on r given that our re-fit model assumes a single A d value applies to both the smaller BICEP2 / Keck fi eld and the larger BICEP3 fi eld.”
hedgedconditional- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it.
- The authors state this as an assumption: The re-fit model assumes a single A_d value applies to both the smaller BICEP2/Keck field and the larger BICEP3 field.
In the paper
“Other additive systematic effects including EMI, magnetic, thermal, and other scan-synchronous sources of residual contamination, and ghost beams, were studied in Ref. [34] and upper limits placed on their contributions equivalent to r < 10 -4 , except in the case of EMI contamination from the satellite uplink transmitter, which was bounded at r < 1 . 7 × 10 -3 with 95% confidence.”
What the sources say
- Not matchedcites [34]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: unclear — It is unclear whether the paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
- Not matched
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“The driving factor in this improvement in the recovered bias is the inclusion of BICEP3 , which demonstrates lower differential beam power than Keck and BICEP2 , both before and after deprojection.”
boosteddirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
What the paper did — it cites no source for this, so there is none to check. The quote shows it is in the paper.
In the paper
“Levels of these potential sources of contamination have been monitored throughout collection of the current dataset (including EMI reduction from additional shielding at the satellite uplink), and contributions from these effects remain negligible.”
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
The authors state this as an assumption.
For dust, EE/BB = 2.
“under the assumption that EE/BB = 2 for dust, as is known to be close to the case [23, 24]”
“under the assumption that EE/BB = 2 for dust”
The authors state this as an assumption.
The synchrotron frequency spectrum is a simple power law A_sync ∝ ν^β_s.
“assuming a simple power law for the frequency spectral behavior A sync ∝ ν β s”
The authors state this as an assumption.
The dust spatial power spectrum is a power law D_ℓ ∝ ℓ^α_d.
“The spatial power spectrum is taken as a power law D ℓ ∝ ℓ α d marginalizing uniformly over the (generous) range -1 < α d < 0”
The authors state this as an assumption.
The synchrotron spatial power spectrum is a power law D_ℓ ∝ ℓ^α_s.
“The spatial power spectrum is taken as a power law D ℓ ∝ ℓ α s marginalizing over the range -1 < α s < 0 [32].”
The authors state this as an assumption.
The power spectrum of the polarized dust emission in the BICEP/Keck field follows a power law.
“We note that this figure offers empirical backing for an assumption which we make in our mainline analysis: that the power spectrum of the polarized dust emission in our field follows a power law.”
The authors state this as an assumption.
The dust and synchrotron sky patterns have Gaussian fluctuations.
“The parametric model which we are using, including the approximation of Gaussian fluctuation of the dust (and synchrotron) sky patterns, remains an adequate description of the presently available data.”
The paper relies on this without support.
Dust decorrelation exists in the BICEP/Keck sky patch at some level.
“Nonetheless, decorrelation surely exists in our sky patch at some level-the question is whether it is relevant as compared to the BK18 experimental noise.”
The authors state this as an assumption.
The EE/BB ratios for dust and synchrotron are both exactly 2.
“under the artificial assumption that the EE/BB ratios for dust and synchrotron are both exactly 2”
The authors state this as an assumption.
The re-fit model assumes a single A_d value applies to both the smaller BICEP2/Keck field and the larger BICEP3 field.
“given that our re-fit model assumes a single A d value applies to both the smaller BICEP2 / Keck fi eld and the larger BICEP3 fi eld.”
The paper relies on this without support.
When running on simulations generated according to the model being re-fit, the input parameter values should be recovered in the mean.
“we then have an a priori expectation that the input parameter values should be recovered in the mean.”
The paper relies on this without support.
The Planck 2018 cosmological parameters predict a specific lensing BB spectrum as used in the BK18 baseline analysis.
“The Planck 2018 cosmological parameters predict a specific lensing BB spectrum as used in the 'BK18 baseline' analysis described above.”
Citations
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A Probe of Primordial Gravity Waves and Vorticity
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Self-citation
Cited by
Sorted by citations
Items 801–900 of 1,009
Warm inflation in Weyl geometric gravity
Huang, R., Harko, T., Liang, S., et al. (2026) · The European Physical Journal C · doi:10.1140/epjc/s10052-026-15860-4 · Cited by 1
“Several recent papers have examined inflation models in light of the ACT data [37–47], with particular focus on the higher scalar spectral index.”
Masubuchi, H., Narita, Y., & Yin, W. (2026) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2026/06/090 · Cited by 1
The art of simulating the early Universe. Part II. Non-canonical cases & gravitational waves
Baeza-Ballesteros, J., Figueroa, D. G., Florio, A., Lizarraga, J., Loayza, N., Marschall, K., Opferkuch, T., Stefanek, B. A., Torrentí, F., & Urio, A. (2026) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2026/06/087 · Cited by 1
Cosmic strings and domain walls: the impact of CMB B -mode data
Caloni, L., Ferreira, R. Z., Sousa, L., et al. (2026) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2026/07/018 · Cited by 1
“03 , which is within the 95% credible upper limit obtained from BK18 [18] (see [72] for a stronger bound on r obtained including additional datasets).”
InfluentialNojiri, S., Odintsov, S. D., & Oikonomou, V. K. (2026) · Fortschritte der Physik · doi:10.1002/prop.70137 · Cited by 1
“The EoS parameter of the two theories is significantly constrained from the updated Planck/BICEP data, which constrain the tensor-to-scalar ratio as [ 72 ] 𝑟 0 .”
Blind mitigation of foreground-induced biases on primordial B modes for ground-based CMB experiments
Mustafa, A., Carones, A., Krachmalnicoff, N., et al. (2026) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2026/08/014 · Cited by 1
“This challenge is already faced by current ground-based experiments, such as BI-CEP/Keck [6] and SO [5].”
Resilience of primordial black hole formation from inflation with a light spectator field
Anonymous, Geller, S. R., Ireland, Z., Kaiser, D. I., McDonough, E., & Wittmeier, K. A. (2026) · Physical review. D/Physical review. D. · doi:10.1103/9rb7-qh69 · Cited by 2
“In each case involving the spectator field, predictions for CMB observables and for PBHs relevant for dark matter remain in strong agreement with CMB measurements [40–43] and PBH constraints [8– 17].”
Primordial black holes from inflation with a spectator field
Anonymous, Geller, S. R., Kaiser, D. I., & McDonough, E. (2026) · Physical review. D/Physical review. D. · doi:10.1103/gwfm-jx9r · Cited by 3
“001 [62–64].”
Squeezing down the Theory Space for Cosmic Inflation
Meerburg, P. D. (2021) · Physics · doi:10.1103/physics.14.135 · Cited by 1
“The BICEP/Keck Collaboration, which has been a frontrunner in the search for this illustrious signal, reports on its latest data set, finding no evidence of gravitational waves [1].”
BackgroundCosmology application of the astrophysics originated gravitational wave
YanRu, S., RenJie, W., ShiJie, L., et al. (2022) · Zhongguo kexue. Wulixue Lixue Tianwenxue · doi:10.1360/sspma-2021-0365 · Cited by 1
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“14 for N ∼ 55 and the inflation with a quadratic potential is ruled out by the Planck and BICEP/Keck experiments [6, 7].”
BackgroundResultStarobinsky–Bel–Robinson Gravity
Ketov, S. V. (2022) · Universe · doi:10.3390/universe8070351 · Cited by 1
“The action (1) is also well phenomenologically motivated due to its excellent agreement with WMAP/Planck/BICEP/KECK precision measurements of the cosmic microwave background radiation [3].”
BackgroundNishinomiya, Y., Kusaka, A., Kiuchi, K., et al. (2022) · Journal of Low Temperature Physics · doi:10.1007/s10909-022-02864-z · Cited by 1
Self-citationThe non-thermal secondary CMB anisotropies from a cosmic distribution of radio galaxy lobes
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Slow-roll inflation in Palatini F(R) gravity
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Palatini formulation for gauge theory: implications for slow-roll inflation
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Origin of neutrino masses, dark matter, leptogenesis, and inflation in a seesaw model with triplets
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“which are allowed by the present experimental data [45, 46, 82] as shown in Fig.”
BackgroundMethodScaling behavior of observables as a model characteristic in multifield inflation
Lynker, M., & Schimmrigk, R. (2023) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2023/04/039 · Cited by 1
“The most stringent of these constraints are currently provided by the Planck probe in combination with the BICEP/Keck experiment [8], although other ground based observatories, already operating or coming on line in the near future, will improve these results [9–11].”
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Freeze-in baryogenesis and early matter domination
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“More recently BICEP2 presented the bound r 0.036 (95% CL) at k = 0.05 Mpc−1 [20] and, future CMB-Stage 4 experiments [33] will have the sensitivity to detect a r > 0.003 signal.”
BackgroundInfluentialInflationary α-attractor models with singular derivative of potential
Kubota, K.-I., Matsui, H., & Terada, T. (2023) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2023/07/011 · Cited by 1
“Then, we compare them with the observational CMB constraints [1, 44].”
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Probing the speed of gravitational waves beyond general relativity from CMB observations
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Observational constraints on asymptotic safety inflation in gravity’s rainbow
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Loop Quantum Cosmology: Relation Between Theory and Observations
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“In this regime they affect cosmological observables, most notably the B -mode polarisation of the Cosmic Microwave Background (CMB) anisotropies [8, 9], which is the target of a massive observational program; see e.g. [10, 11, 12].”
BackgroundElectromagnetic Waves in Cosmological Space–Time II. Luminosity Distance
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Dark energy due to quantum corrections to effective potential
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Power spectra in double-field inflation using renormalization-group techniques
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“Nevertheless, the modification of the single-field quadratic inflation are not sufficient to withstand comparison with the Planck [5] and BICEP/Keck [28] collaborations. λ and ϱ to some values.”
Gravitational dark matter production in supergravity α-attractor inflation
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Dynamical dark energy in the no-scale Brans–Dicke gravity
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“This is of particular importance when trying to observe the primordial B modes, sourced by the gravitational waves created by inflation: constraints on the tensor to scalar ratio are limited by the variance from the secondary B modes created by lensing [2, 3].”
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“• Tensor-to-scalar ratio The recent BICEP/Keck result [2] gives the upper bound on the tensor-to-scalar ratio as r0.”
BackgroundMethodInfluentialRemoval of point source leakage from time-order data filtering
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Looking inside the Swampland from Warm Inflation: Dissipative Effects in De Sitter Expansion
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A Measurement of Gravitational Lensing of the Cosmic Microwave Background Using SPT-3G 2018 DataPreprint
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“With SPT-3G ’s full-survey lensing map, we expect to improve BICEP Array’s r uncertainty by a factor of about 2.5, reaching σ ( r ) of about 0.003.”
InfluentialSelf-citation‘Best view ever’: observatory will map Big Bang’s afterglow in new detail
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Relic gravitons at intermediate frequencies and the expansion history of the Universe
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Polarization angle requirements for CMB B-mode experiments. Application to the LiteBIRD satellite
Vielva, P., Martínez-González, E., Casas, F. J., et al. (2022) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2022/04/029
Self-citationThe $$R^2$$ R 2 -Higgs inflation with two Higgs doublets
Lee, S. M., Modak, T., Oda, K.-Y., & Takahashi, T. (2022) · DOAJ (DOAJ: Directory of Open Access Journals) · doi:10.1140/epjc/s10052-021-09978-w · Cited by 10
CCAT-Prime: Characterization of the First 280 GHz MKID Array for Prime-Cam
Choi, S. K., Duell, C. J., Austermann, J. E., et al. (2022) · Journal of Low Temperature Physics · doi:10.1007/s10909-022-02787-9
Self-citationA demonstration of spectral level reconstruction of intrinsic B-mode power
Pal, B. K. (2023) · Pramana · doi:10.1007/s12043-022-02509-6
Constraining $\alpha$-attractor models from reheating.Preprint
Germán, G. (2021) · arXiv (Cornell University)
Signatures of Primordial Gravitational Waves on the Large-Scale Structure of the Universe
Bari, P., Ricciardone, A., Bartolo, N., Bertacca, D., & Matarrese, S. (2022) · Physical Review Letters · doi:10.1103/physrevlett.129.091301 · Cited by 23
The quantum de Sitter root of quasi de Sitter observables: a pedagogical reviewPreprint
Gómez, C., & Jiménez, R. (2021) · arXiv (Cornell University) · doi:10.48550/arxiv.2111.05380
“Figure adapted from the latest BICEP/Keck Array results [58].”
MethodViscous absorption of ultra-high-frequency gravitons
Massimo Giovannini, A. (2022) · Physics Letters B · doi:10.1016/j.physletb.2022.137071
Matter, Dark Matter and Quartic Potential Generated by Unstable Confinement of Quarks
Matsson, L. (2021) · Journal of Modern Physics · doi:10.4236/jmp.2021.1213109
Physics news on the Internet (based on electronic preprints)
Eroshenko, Y. N. (2021) · Physics-Uspekhi · doi:10.3367/ufne.2021.10.039086
Constant-Roll Inflation Driven by Holographic Dark EnergyPreprint
Mohammadi, A. (2022) · SSRN Electronic Journal · doi:10.2139/ssrn.4077496
Finite inflation in curved space
Hergt, L. T., Agocs, F. J., Handley, W. J., Hobson, M., & Lasenby, A. N. (2022) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.106.063529
Physics of the early Universe: non-singular cosmologies and multifield inflation
Chiovoloni, R. (2022) · Cronfa (Swansea University) · doi:10.23889/suthesis.60118
2022 upgrade and improved low frequency camera sensitivity for CMB observation at the South Pole
Soliman, A., Ade, P. A. R., Ahmed, Z., et al. (2022) · Millimeter, Submillimeter, and Far-Infrared Detectors and Instrumentation for Astronomy XI · doi:10.1117/12.2628058
“To date, BICEP/Keck (BK) program has placed the strongest constrains on the amplitude of PGWs, the tensor-to-scalar ratio r .(2) The current sensitivity is limited by the modeling of both gravitational lensing and polarized Galactic foregrounds.”
BackgroundSelf-citationScalar Induced Gravitational Waves from Warm InflationPreprint
Arya, R., & Mishra, A. K. (2022) · SSRN Electronic Journal · doi:10.2139/ssrn.4185374
$$e^+e^-$$ annihilation on the stochastic background of primordial gravitational waves with BKP18
Malsawmtluangi, N. (2022) · The European Physical Journal C · doi:10.1140/epjc/s10052-022-10978-7
Formal theory: status and outlook
Quevedo, F. (2022) · International Conference on High Energy Physics (ICHEP) · doi:10.22323/1.414.0027
Reheating constraints in modified natural inflation with the decaying inflaton
Yusmantoro, Y., Achmad, A., & Julianto, R. (2023) · International Journal of Modern Physics D · doi:10.1142/s0218271823500359
k -essence induced by derivative couplings of the inflaton
Hung, Y. S., & Miao, S. P. (2023) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.107.103533
Warm inflation with bulk viscous pressure for different solutions of an anisotropic universePreprint
Shokri, M., Sadeghi, J., Herrera, R., et al. (2023) · Research Square · doi:10.21203/rs.3.rs-3116831/v1
Datta, R., Brewer, M. K., Couto, J. D., et al. (2023) · arXiv (Cornell University) · doi:10.13016/m2linh-kp1b
Self-citationReport on scipost_202209_00065v2
Figueroa, D. G., Florio, A., Opferkuch, T., et al. (2023) · SciPost Physics · doi:10.21468/scipost.report.6927
Report on scipost_202209_00065v1
Figueroa, D. G., Florio, A., Opferkuch, T., et al. (2022) · SciPost Physics · doi:10.21468/scipost.report.6270
Report on scipost_202209_00065v1
Figueroa, D. G., Florio, A., Opferkuch, T., et al. (2022) · SciPost Physics · doi:10.21468/scipost.report.6370
Fong, C. S. (2023) · Cadernos de Astronomia · doi:10.47456/cad.astro.v4n2.41796
física da radiação cósmica de fundo em micro-ondas
Guimarães, L. F. (2023) · Cadernos de Astronomia · doi:10.47456/cad.astro.v4n2.41639
Ultraheavy FIMP dark matter and conformal sectors
Ismail, A. (2023) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.108.095049
Non-minimally coupled scalar field and scaling symmetry in a cosmological background
Matwi, M., & Nozari, K. (2023) · Physica Scripta · doi:10.1088/1402-4896/ad15d6
B-mode polarization forecasts for GreenPol
Fuskeland, U., Kaplan, A., Wehus, I. K., et al. (2024) · Astronomy and Astrophysics · doi:10.1051/0004-6361/202347393
Brito, F. A., Rocha, J. C. M., Lemos, A. S., et al. (2025) · Modern Physics Letters A · doi:10.1142/s0217732325501974
“In the following subsection, we must apply these results by considering the β -exponential potential, aiming to find constraints for this theoretical model from Planck data [24, 25].”
InfluentialReheating constraints to Palatini Coleman-Weinberg inflation
Bostan, N. (2024) · TURKISH JOURNAL OF PHYSICS · doi:10.55730/1300-0101.2754
Development of generic no-scale inflation
Wu, L., Shen, J.-K., Li, T., et al. (2024) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2024/07/036
“10 × 10 − 9 [4, 5] by formulating the parameter V 0 .”
Swampland Program, Extra Dimensions, and Supersymmetry Breaking
Anchordoqui, L. A., Ignatios Antoniadis, A., Laboratoire de Physique Théorique et Hautes Énergies - LPTHE, S. U., et al. (2023) · Letters in High Energy Physics · doi:10.31526/acp.bsm-2023.12
Scalaron Decay in Perturbative Quantum Gravity
Latosh, B. (2023) · Журнал Экспериментальной и Теоретической Физики · doi:10.31857/s0044451023050024
Inflation in simple one-loop effective potentials of perturbative quantum gravity
Arbuzov, A. B., Kuznetsov, D., Latosh, B., & Shmidt, V. (2024) · International Journal of Modern Physics D · doi:10.1142/s0218271824500287
“These parameters are well constrained by the present observational data [6, 7, 8, 9, 10]:”
BackgroundYukawa coupling and one loop inflation in the light of CMB
Anupama, B., & Suresh, P. K. (2026) · Indian Journal of Physics · doi:10.1007/s12648-026-04220-3
“5 [27, 28, 29] is much higher than the upper limit derived from BK18 (0.036) [40], PR 4 + BK18 (0.032) [41], LiteBIRD [42] and CMB S4 (0.004, future projected estimate) [11].”
InfluentialInflation as a One-Loop Effect
Arbuzov, A. B., Kuznetsov, D., Latosh, B., & Shmidt, V. M. (2024) · Physics of Particles and Nuclei Letters · doi:10.1134/s1547477124700444
The Simons Observatory: calibration and characterization of the first small-aperture telescope
Crowley, K. T., Arnold, K., Galitzki, N. B., et al. (2024) · doi:10.1117/12.3020564
Lightweight foam-based reflective thin film panels for radio telescopes
Cheung, K. P. E., & Li, H.-B. (2024) · Space Telescopes and Instrumentation: Optical, Infrared, and Millimeter Wave · doi:10.1117/12.3018255
Unification: inflation and dark epochs from multi-field theory.Preprint
Guendelman, E. I., & Herrera, R. (2024) · Preprints.org · doi:10.20944/preprints202406.1473.v1
Systematic Effects on Lensing Reconstruction from a Patchwork of CMB Polarization Maps
Nagata, R., & Namikawa, T. (2024) · Progress of Theoretical and Experimental Physics · doi:10.1093/ptep/ptae117
Self-citationBhaumik, A., & Pal, S. (2024) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.110.043511
“The latest observations of Planck 2018 [66] and BICEP/Keck [89] jointly yield an upper limit of r < 0.”
MethodA skewed perspective on the universe
Flöss, T. (2024) · University of Groningen research database (University of Groningen / Centre for Information Technology) · doi:10.33612/diss.1084344889
Cembranos, J. A. R., & Karčiauskas, M. (2024) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2024/08/051
Cosmology of the Early Universe with AxionsPreprint
Heredia, J. R. T. (2024) · SSRN Electronic Journal · doi:10.2139/ssrn.4962096
Ade, P. A. R., Ahmed, Z., Amiri, M., et al. (2026) · The Astrophysical Journal · doi:10.3847/1538-4357/ae486d
Self-citationSpectrum of primordial gravitational waves in the presence of a cosmic string
Galeh, S. A. A., Abbassi, A. M., & Abbassi, M. H. (2024) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2024/11/048
“05 Mpc − 1 [3].”
Double-well inflation: observational constraints and theoretical implications
Rodrigues, G., Rodrigues, J. G., dos Santos, F. B. M., et al. (2024) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2024/11/055
Quantum Gravity and Scale Symmetry in Cosmology
WETTERICH, C. (2024) · Springer eBooks · doi:10.1007/978-981-99-7681-2_26
Metadata
- Authors
- Ade, P. A. R., Ahmed, Z., Amiri, M., Barkats, D., Thakur, R. B., Bischoff, C. A., Beck, D., Bock, J. J., Boenish, H., Bullock, E., Buza, V., Cheshire, J. R., Connors, J., Cornelison, J., Crumrine, M., Cukierman, A., Denison, E. V., Dierickx, M., Duband, L., Eiben, M., Fatigoni, S., Filippini, J. P., Fliescher, S., Goeckner-Wald, N., Goldfinger, D. C., Grayson, J., Grimes, P., Hall, G., Halal, G., Halpern, M., Hand, E., Harrison, S., Henderson, S., Hildebrandt, S. R., Hilton, G. C., Hubmayr, J., Hui, H., Irwin, K. D., Kang, J., Karkare, K. S., Karpel, E., Kefeli, S., Kernasovskiy, S. A., Kovac, J. M., Kuo, C. L., Lau, K., Leitch, E. M., Lennox, A., Megerian, K. G., Minutolo, L., Moncelsi, L., Nakato, Y., Namikawa, T., Nguyen, H. T., O’Brient, R., Ogburn, R. W., Palladino, S., Prouve, T., Pryke, C., Racine, B., Reintsema, C. D., Richter, S., Schillaci, A., Schwarz, R., Schmitt, B. L., Sheehy, C. D., Soliman, A., Germaine, T. S., Steinbach, B., Sudiwala, R. V., Teply, G. P., Thompson, K. L., Tolan, J. E., Tucker, C., Turner, A. D., Umiltà, C., Vergès, C., Vieregg, A. G., Wandui, A., Weber, A. C., Wiebe, D. V., Willmert, J., Wong, C. L., Wu, W. L. K., Yang, H., Yoon, K. W., Young, E., Yu, C., Zeng, L., Zhang, C., Zhang, S., & BICEP/<i>Keck</i> Collaboration
- Affiliations
- Cardiff University (GB)
- SLAC National Accelerator Laboratory (US)
- University of British Columbia (CA)
- Center for Astrophysics Harvard & Smithsonian (US)
- California Institute of Technology (US)
- University of Cincinnati (US)
- University of Minnesota (US)
- University of Chicago (US)
- National Institute of Standards and Technology (US)
- Commissariat à l'Énergie Atomique et aux Énergies Alternatives (FR)
- University of Illinois Urbana-Champaign (US)
- Stanford University (US)
- Harvard University (US)
- Jet Propulsion Laboratory (US)
- Kavli Institute for the Physics and Mathematics of the Universe (JP)
- Service des Basses Températures, Commissariat à l’Energie Atomique, 38054 Grenoble, France
- Centre National de la Recherche Scientifique (FR)
- Brookhaven National Laboratory (US)
- ORCID
- Ade, P. A. R.
- Ahmed, Z.
- Barkats, D.
- Bischoff, C. A.
- Beck, D.
- Bock, J. J.
- Buza, V.
- Cheshire, J. R.
- Cukierman, A.
- Dierickx, M.
- Eiben, M.
- Filippini, J. P.
- Goldfinger, D. C.
- Grimes, P.
- Halal, G.
- Halpern, M.
- Henderson, S.
- Hildebrandt, S. R.
- Irwin, K. D.
- Karkare, K. S.
- Kovac, J. M.
- Kuo, C. L.
- Leitch, E. M.
- Nakato, Y.
- Namikawa, T.
- Ogburn, R. W.
- Pryke, C.
- Racine, B.
- Schillaci, A.
- Sudiwala, R. V.
- Thompson, K. L.
- Tolan, J. E.
- Vergès, C.
- Vieregg, A. G.
- Wandui, A.
- Wiebe, D. V.
- Willmert, J.
- Wu, W. L. K.
- Young, E.
- Yu, C.
- Zeng, L.
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 2021-10-04
- Volume
- 127
- Issue
- 15
- Pages
- 151301-151301
- ISSN
- 0031-9007 (ISSN-L)
- 1079-7114
- OpenAlex
- W3202102945
- Semantic Scholar
- 93637369c8e398b920a6f82f83adf5ffc4fbba76
- Cited by
- 1,014
- References
- 57
- Citations by year
- 2026: 163 · 2025: 253 · 2024: 218 · 2023: 203 · 2022: 162 · 2021: 15
- FWCI
- 80.49
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Licence
- Locations
- Physical Review Letters (publishedVersion)
- PubMed (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- CaltechAUTHORS (California Institute of Technology) (submittedVersion)
- HAL AMU (submittedVersion)
- OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information) (submittedVersion)
- arXiv (Cornell University)
- Funders
- National Science Foundation (0742818, 0742592, 1044978, 1110087, 1145172, 1145143, 1145248, 1639040, 1638957, 1638978, 1638970)
- W. M. Keck Foundation
- Jet Propulsion Laboratory
- National Aeronautics and Space Administration (06-ARPA206-0040, 10-SAT10-0017, 12-SAT12-0031, 14-SAT14-0009, 16-SAT-16-0002)
- Gordon and Betty Moore Foundation
- Canada Foundation for Innovation
- University of British Columbia
- Science and Technology Facilities Council (ST/N000706/1)
- Faculty of Arts and Sciences, Harvard University
- U.S. Department of Energy
- Office of Science
- Topics
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Cosmology and Gravitation Theories
- Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Dark Matter and Cosmic Phenomena
- Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Noncommutative and Quantum Gravity Theories
- Keywords
- primordial gravitational waves, BICEP2, Keck Array, CMB polarization, tensor-to-scalar ratio, foreground modeling, polarized dust emission, synchrotron radiation, Planck, WMAP
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