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Improved Constraints on Primordial Gravitational Waves using Planck , WMAP, and BICEP/ Keck Observations through the 2018 Observing Season

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Ade, P. A. R., Ahmed, Z., Amiri, M., Barkats, D., Thakur, R. Basu, 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. St., 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·2021·Physical Review Letters

DOI 10.1103/physrevlett.127.151301

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Abstract

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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Written from the paper’s full text.

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.

Model-written summary. Check it against the paper before relying on it.

Integrity signals

Registry

Crossref · 10.1103/physrevlett.127.151301

Cites

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Claims the paper makes

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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
“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.”
Load-bearingStrength:plain· not yet calibrated
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passes
- 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.
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 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.”
Strength:plain· not yet calibrated
Tests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passes
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 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.”
Load-bearingStrength:plain· not yet calibrated
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passes
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 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.”
Strength:plain· not yet calibrated
Tests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passes
- 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.

Show all 73 claims

It may state two separate claims as one. 53
Probably not a substantial claim. 34

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
“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”
Strength:plain· not yet calibratedCausal:direct· not yet calibrated
Tests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passes
It may state two separate claims as one.
In the paper
“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 matched
  Couldn’t be matched to a paper in Crossref, so it can’t be checked.
  cites [24]
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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
“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.”
Strength:hedged· not yet calibratedCausal:direct· not yet calibrated
Tests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passes
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
“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.”
Strength:plain· not yet calibratedCausal:direct· not yet calibrated
Tests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passes
It may state two separate claims as one.
- The authors state this as an assumption: The EE/BB ratios for dust and synchrotron are both exactly 2.
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.”
Load-bearingStrength:plain· not yet calibratedCausal:direct· not yet calibrated
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passes
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.
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 matched
  Couldn’t be matched to a paper in Crossref, so it can’t be checked.
  cites [24]
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Probably not a substantial claim. The paper’s conclusions may not depend on it.
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
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  Couldn’t be matched to a paper in Crossref, so it can’t be checked.
  cites [52]
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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
“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”
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  cites [64]
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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
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  cites [10]
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Probably not a substantial claim.
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
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  cites [9]
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  cites [34]
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Probably not a substantial claim.
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
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  Couldn’t be matched to a paper in Crossref, so it can’t be checked.
  cites [9]
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Probably not a substantial claim. The paper’s conclusions may not depend on it.
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
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  cites [5]
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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
“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].”
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It may state two separate claims as one.
- The authors state this as an assumption: For dust, EE/BB = 2.
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
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  cites [17, Fig. 5]
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Probably not a substantial claim. The paper’s conclusions may not depend on it. 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
“Planck analysis consistently finds approximate power law behavior of both the EE and BB dust spectra with exponents ≈ -0 . 4 [23, 24].”
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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
“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].”
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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.)”
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  cites [30]
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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.”
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  cites [4]
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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
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  cites [2]
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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.”
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  cites [55]
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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
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  cites [30]
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Probably not a substantial claim. The paper’s conclusions may not depend on it. 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
“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].”
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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'.”
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  cites [56]
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Probably not a substantial claim.
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.”
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Probably not a substantial claim. The paper’s conclusions may not depend on it.
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
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  Couldn’t be matched to a paper in Crossref, so it can’t be checked.
  cites [30]
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Probably not a substantial claim. The paper’s conclusions may not depend on it.
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.”
Strength:hedged· not yet calibratedCausal:conditional· not yet calibrated
Tests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passes
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
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  cites [34]
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82 of 82

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.”

11 of 11

Planck 2018 results: VI. Cosmological parameters
Planck Collaboration, Aghanim, N., Akrami, Y., Ashdown, M., Aumont, J., Baccigalupi, C., Ballardini, M., Banday, A. J., Barreiro, R. B., Bartolo, N., et al. (2020) · Astronomy & Astrophysics · doi:10.1051/0004-6361/201833910 · Cited by 14,258
Self-citation
Cosmological parameters from CMB and other data: A Monte Carlo approach
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Self-citation
A Measurement of Excess Antenna Temperature at 4080 Mc/s.
Penzias, A. A., & Wilson, R. W. (1965) · The Astrophysical Journal · doi:10.1086/148307 · Cited by 2,606
Planck 2018 results
Akrami, Y., Arroja, F. M. A., Ashdown, M., Aumont, J., Baccigalupi, C., Ballardini, M., Banday, A. J., Barreiro, R. B., Bartolo, N., Basak, S., et al. (2019) · Astronomy and Astrophysics · doi:10.1051/0004-6361/201833887 · Cited by 2,435
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Detection of B -Mode Polarization at Degree Angular Scales by BICEP2
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Joint Analysis of BICEP2/ Keck Array and Planck Data
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Signature of Gravity Waves in the Polarization of the Microwave Background
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A Probe of Primordial Gravity Waves and Vorticity
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Improved Constraints on Cosmology and Foregrounds from BICEP2 and Keck Array Cosmic Microwave Background Data with Inclusion of 95 GHz Band
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Gravitational lensing effect on cosmic microwave background polarization
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The Quest for B Modes from Inflationary Gravitational Waves
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The Atacama Cosmology Telescope: a measurement of the Cosmic Microwave Background power spectra at 98 and 150 GHz
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A Measurement of the CMB 〈EE〉 Spectrum from the 2003 Flight of BOOMERANG
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IMPROVED MEASUREMENTS OF THE TEMPERATURE AND POLARIZATION OF THE COSMIC MICROWAVE BACKGROUND FROM QUaD
Brown, M. L., Ade, P. A. R., Bock, J. J., Bowden, M., Cahill, G., Castro, P. G., Church, S., Culverhouse, T., Friedman, R. B., Ganga, K. M., et al. (2009) · The Astrophysical Journal · doi:10.1088/0004-637x/705/1/978 · Cited by 257
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Likelihood analysis of CMB temperature and polarization power spectra
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The Python Sky Model: software for simulating the Galactic microwave sky
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BICEP2. II. EXPERIMENT AND THREE-YEAR DATA SET
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Planck intermediate results
Adam, R., Ade, P. A. R., Aghanim, N., Arnaud, M., Aumont, J., Baccigalupi, C., Banday, A. J., Barreiro, R. B., Bartlett, J. G., Bartolo, N., et al. (2015) · Astronomy and Astrophysics · doi:10.1051/0004-6361/201425034 · Cited by 219
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Planck 2018 results
Akrami, Y., Ashdown, M., Aumont, J., Baccigalupi, C., Ballardini, M., Banday, A. J., Barreiro, R. B., Bartolo, N., Basak, S., Benabed, K., et al. (2019) · Astronomy and Astrophysics · doi:10.1051/0004-6361/201832618 · Cited by 200
Planckintermediate results. XXII. Frequency dependence of thermal emission from Galactic dust in intensity and polarization
Ade, P. A. R., Alves, M. I. R., Aniano, G., Armitage-Caplan, C., Arnaud, M., Atrio-Barandela, F., Aumont, J., Baccigalupi, C., Banday, A. J., Barreiro, R. B., et al. (2015) · Astronomy and Astrophysics · doi:10.1051/0004-6361/201424088 · Cited by 187
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Degree Angular Scale Interferometer 3 Year Cosmic Microwave Background Polarization Results
Leitch, E. M., Kovac, J. M., Halverson, N. W., Carlstrom, J. E., Pryke, C. L., & Smith, M. W. E. (2005) · The Astrophysical Journal · doi:10.1086/428825 · Cited by 177
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Planck constraints on the tensor-to-scalar ratio
Tristram, M., Banday, A. J., Gorski, K. M., Keskitalo, R., Lawrence, C. R., Andersen, K. J., Barreiro, R. B., Borrill, J., Eriksen, H. K., Fernández-Cobos, R., et al. (2021) · Astronomy and Astrophysics · doi:10.1051/0004-6361/202039585 · Cited by 164
A Measurement of the Cosmic Microwave Background B-mode Polarization Power Spectrum at Subdegree Scales from Two Years of polarbear Data
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BICEP2/KECK ARRAY V: MEASUREMENTS OFB-MODE POLARIZATION AT DEGREE ANGULAR SCALES AND 150 GHz BY THE KECK ARRAY
Ade, P. A. R., Ahmed, Z., Aikin, R. W., et al. (2015) · The Astrophysical Journal · doi:10.1088/0004-637x/811/2/126 · Cited by 123
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Implications of the Cosmic Background Imager Polarization Data
Sievers, J. L., Achermann, C., Bond, J. R., Bronfman, L., Bustos, R., Contaldi, C., Dickinson, C., Ferreira, P. G., Jones, M. E., Lewis, A., et al. (2007) · The Astrophysical Journal · doi:10.1086/510504 · Cited by 116
SECOND SEASON QUIET OBSERVATIONS: MEASUREMENTS OF THE COSMIC MICROWAVE BACKGROUND POLARIZATION POWER SPECTRUM AT 95 GHz
Araujo, D., Bischoff, C. A., Brizius, A., Buder, I., Chinone, Y., Cleary, K., Dumoulin, R. N., Kusaka, A., Monsalve, R. A., Næss, S., et al. (2012) · The Astrophysical Journal · doi:10.1088/0004-637x/760/2/145 · Cited by 103
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ANTENNA-COUPLED TES BOLOMETERS USED IN BICEP2,Keck Array, AND SPIDER
Ade, P. A. R., Aikin, R. W., Amiri, M., et al. (2015) · The Astrophysical Journal · doi:10.1088/0004-637x/812/2/176 · Cited by 94
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BICEP Array: a multi-frequency degree-scale CMB polarimeter
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Measurements of B -mode polarization of the cosmic microwave background from 500 square degrees of SPTpol data
Sayre, J. T., Reichardt, C. L., Henning, J. W., Ade, P. A. R., Anderson, A. J., Austermann, J. E., Avva, J. S., Beall, J. A., Bender, A. N., Benson, B. A., et al. (2020) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.101.122003 · Cited by 92
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S–PASS view of polarized Galactic synchrotron at 2.3 GHz as a contaminant to CMB observations
Krachmalnicoff, N., Carretti, E., Baccigalupi, C., Bernardi, G., Brown, S., Gaensler, B., Haverkorn, M., Kesteven, M., Perrotta, F., Poppi, S., et al. (2018) · Astronomy & Astrophysics · doi:10.1051/0004-6361/201832768 · Cited by 86
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Bischoff, C. A., Hyatt, L., McMahon, J. J., Nixon, G. W., Samtleben, D. F. E., Smith, K. M., Vanderlinde, K., Barkats, D., Farese, P. C., Gaier, T., et al. (2008) · The Astrophysical Journal · doi:10.1086/590487 · Cited by 78
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The structure and statistics of interstellar turbulence
Kritsuk, A. G., Ustyugov, S. D., & Norman, M. L. (2017) · New Journal of Physics · doi:10.1088/1367-2630/aa7156 · Cited by 78
A Measurement of the Degree-scale CMB B-mode Angular Power Spectrum with Polarbear
Adachi, S., Faúndez, M. A. O. A., Arnold, K., Baccigalupi, C., Barron, D. R., Beck, D., Beckman, S., Bianchini, F., Boettger, D., Borrill, J., et al. (2020) · The Astrophysical Journal · doi:10.3847/1538-4357/ab8f24 · Cited by 71
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DEGREE-SCALE COSMIC MICROWAVE BACKGROUND POLARIZATION MEASUREMENTS FROM THREE YEARS OF BICEP1 DATA
Barkats, D., Aikin, R. W., Bischoff, C. A., Buder, I., Kaufman, J. P., KEATING, B. G., Kovac, J. M., Su, M., Ade, P. A. R., Battle, J., et al. (2014) · The Astrophysical Journal · doi:10.1088/0004-637x/783/2/67 · Cited by 70
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Bicep2. III. INSTRUMENTAL SYSTEMATICS
Ade, P. A. R., Aikin, R. W., Barkats, D., et al. (2015) · The Astrophysical Journal · doi:10.1088/0004-637x/814/2/110 · Cited by 63
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Planck intermediate results
Aghanim, N., Ashdown, M., Aumont, J., et al. (2016) · Astronomy and Astrophysics · doi:10.1051/0004-6361/201629164 · Cited by 63
SPATIAL VARIATIONS IN THE SPECTRAL INDEX OF POLARIZED SYNCHROTRON EMISSION IN THE 9 yr WMAP SKY MAPS
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Receiver development for BICEP Array, a next-generation CMB polarimeter at the South Pole
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Dust-Polarization Maps for Local Interstellar Turbulence
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A demonstration of improved constraints on primordial gravitational waves with delensing
Ade, P. A. R., Ahmed, Z., Amiri, M., Anderson, A. J., Austermann, J. E., Avva, J. S., Barkats, D., Thakur, R. B., Beall, J. A., Bender, A. N., et al. (2021) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.103.022004 · Cited by 43
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BICEP2/KECK ARRAY. VII. MATRIX BASED E/B SEPARATION APPLIED TO BICEP2 AND THE KECK ARRAY
Ade, P. A. R., Ahmed, Z., Aikin, R. W., et al. (2016) · The Astrophysical Journal · doi:10.3847/0004-637x/825/1/66 · Cited by 25
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Panopoulou, G. V., & Lenz, D. (2020) · The Astrophysical Journal · doi:10.3847/1538-4357/abb6f5 · Cited by 24
BICEP2/Keck Array XI: Beam Characterization and Temperature-to-Polarization Leakage in the BK15 Data Set
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Constraints on the spectral index of polarized synchrotron emission from WMAP and Faraday-corrected S-PASS data
Fuskeland, U., Andersen, K. J., Aurlien, R., et al. (2020) · Astronomy and Astrophysics · doi:10.1051/0004-6361/202037629 · Cited by 22

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Probing cosmic inflation with the LiteBIRD cosmic microwave background polarization survey
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Improved limits on the tensor-to-scalar ratio using BICEP and P l a n c k data
Tristram, M., Banday, A. J., Gorski, K. M., Keskitalo, R., Lawrence, C. R., Andersen, K. J., Barreiro, R. B., Borrill, J., Colombo, L. P. L., Eriksen, H. K., et al. (2022) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.105.083524 · Cited by 266
The Atacama Cosmology Telescope: DR6 power spectra, likelihoods and ΛCDM parameters
Louis, T., Posta, A. L., Atkins, Z., Jense, H. T., Abril-Cabezas, I., Addison, G. E., Ade, P. A. R., Aiola, S., Alford, T., Alonso, D., et al. (2025) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2025/11/062 · Cited by 239
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See all 1,014

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
DOI: 10.1103/physrevlett.127.151301
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: link.aps.org/licenses/aps-default-license (vor)
link.aps.org/licenses/aps-default-accepted-manuscript-license (am, 365 d)
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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Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.

A language model drew the claims from the paper on 2026-10-23, under version 3 of the claim definition (model deepseek-v4.1-flash, prompt extract-v3).

A second model labelled each claim on 2026-10-23 (model jev-1.13-20260917, definition revision gold-guideline-v0.2).

Statistics and arithmetic are recomputed, not judged.

Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.

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Improved Constraints on Primordial Gravitational Waves using Planck , WMAP, and BICEP/ Keck Observations through the 2018 Observing Season

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