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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
Lewis, A., & Bridle, S. (2002) · Physical Review D · doi:10.1103/physrevd.66.103511 · Cited by 3,495
NINE-YEAR WILKINSON MICROWAVE ANISOTROPY PROBE ( WMAP ) OBSERVATIONS: FINAL MAPS AND RESULTS
Bennett, C. L., Larson, D., Weiland, J. L., Jarosik, N., Hinshaw, G., Odegard, N., Smith, K. M., Hill, R. S., Gold, B., Halpern, M., et al. (2013) · The Astrophysical Journal Supplement Series · doi:10.1088/0067-0049/208/2/20 · Cited by 2,639
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
Self-citation
Detection of B -Mode Polarization at Degree Angular Scales by BICEP2
Ade, P. A. R., Aikin, R. W., Barkats, D., Benton, S. J., Bischoff, C. A., Bock, J. J., Brevik, J. A., Buder, I., Bullock, E., Dowell, C. D., et al. (2014) · Physical Review Letters · doi:10.1103/physrevlett.112.241101 · Cited by 1,572
Self-citation
Joint Analysis of BICEP2/ Keck Array and Planck Data
Ade, P. A. R., Aghanim, N., Ahmed, Z., Aikin, R. W., Alexander, K. D., Arnaud, M., Aumont, J., Baccigalupi, C., Banday, A. J., Barkats, D., et al. (2015) · Physical Review Letters · doi:10.1103/physrevlett.114.101301 · Cited by 1,013
Self-citation
Signature of Gravity Waves in the Polarization of the Microwave Background
Seljak, U., & Zaldarriaga, M. (1997) · Physical Review Letters · doi:10.1103/physrevlett.78.2054 · Cited by 982
A Probe of Primordial Gravity Waves and Vorticity
Kamionkowski, M., Kosowsky, A. B., & Stebbins, A. J. (1997) · Physical Review Letters · doi:10.1103/physrevlett.78.2058 · Cited by 838
Improved Constraints on Cosmology and Foregrounds from BICEP2 and Keck Array Cosmic Microwave Background Data with Inclusion of 95 GHz Band
Ade, P. A. R., Ahmed, Z., Aikin, R. W., Alexander, K. D., Barkats, D., Benton, S. J., Bischoff, C. A., Bock, J. J., Bowens-Rubin, R., Brevik, J. A., et al. (2016) · Physical Review Letters · doi:10.1103/physrevlett.116.031302 · Cited by 649
Self-citation

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Items 301–400 of 1,009

Constant-roll inflation driven by holographic dark energy
Mohammadi, A. (2022) · Physics of the Dark Universe · doi:10.1016/j.dark.2022.101055 · Cited by 14
Superheavy dark matter from the natural inflation in light of the highest-energy astroparticle events
Murase, K., Narita, Y., & Yin, W. (2025) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2025/10/109 · Cited by 13
QUBIC VI: Cryogenic half wave plate rotator, design and performance
D’Alessandro, G., Mele, L., Columbro, F., et al. (2022) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2022/04/039 · Cited by 13
Self-citation
Constraining the Barbero-Immirzi parameter from the duration of inflation in loop quantum cosmology
Barboza, L. N., Levy, G. L. L. W., Graef, L. L., & Ramos, R. O. (2022) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.106.103535 · Cited by 13
“The new data release from BICEP/Keck [54] strengthened the bounds on the tensor-to-scalar ratio r, putting severe constraints in the full class of monomial potentials, showing that they are disfavored in the context of standard inflation.”
MethodInfluential
Shape of CMB lensing in the early dark energy cosmology
Ye, G., Jiang, J.-Q., & Yun-song Piao, A. (2023) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.108.063512 · Cited by 13
VISH ν : solving five Standard Model shortcomings with a Poincaré-protected electroweak scale
Sopov, A. H., & Volkas, R. R. (2023) · Physics of the Dark Universe · doi:10.1016/j.dark.2023.101381 · Cited by 13
Hadrophobic axion from a GUT
Takahashi, F., & Yin, W. (2024) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.109.035024 · Cited by 13
Minimizing the tensor-to-scalar ratio in single-field inflation models
Wolf, W. J. (2024) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.110.043521 · Cited by 13
Gravitational-wave background in bouncing models from semi-classical, quantum and string gravity
Ben-Dayan, I., Calcagni, G., Gasperini, M., Mazumdar, A., Pavone, E., Thattarampilly, U., & Verma, A. (2024) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2024/09/058 · Cited by 13
Scalar induced gravitational waves in f(R) gravity
Zhou, J., Kuang, Y., Wu, D., et al. (2024) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2024/12/021 · Cited by 13
“Over the past decade, gravitational waves have become a major research topic in cosmology, astrophysics, and astronomy [3–5].”
Background
Third-order corrections to the slow-roll expansion: Calculation and constraints with Planck, ACT, SPT, and BICEP/Keck
Ballardini, M., Davoli, A., & Sirletti, S. S. (2025) · Physics of the Dark Universe · doi:10.1016/j.dark.2025.101813 · Cited by 13
How deep is the dip and how tall are the wiggles in inflationary power spectra?
Briaud, V., Καράμ, Α., Koivunen, N., Tomberg, E., Veermäe, H., & Vennin, V. (2025) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2025/05/097 · Cited by 13
“1 × 10 − 9 in agreement with CMB measurements [109, 110].”
Isotropic cosmic birefringence from string axion domain walls without cosmic strings and DESI results
Lee, J., Murai, K., Takahashi, F., & Yin, W. (2025) · Physical review. D/Physical review. D. · doi:10.1103/pjf4-sn4v · Cited by 13
Inflation story: slow-roll and beyond
Hazra, D. K., Paoletti, D., Debono, I., Shafieloo, A., Smoot, G. F., & Starobinsky, A. A. (2021) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2021/12/038 · Cited by 13
“2BK18 [105] data was released after the release of the paper.”
Background
Inflation and primordial fluctuations in F(T) gravity’s rainbow
Leyva, Y., Leiva, C., Otalora, G., & Saavedra, J. (2022) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.105.043523 · Cited by 14
Reheating constraints on modified single-field natural inflation models
Zhou, H., Yu, Q., Pan, Y., Zhou, R., & Cheng, W. S. (2022) · The European Physical Journal C · doi:10.1140/epjc/s10052-022-10559-8 · Cited by 13
“Unfortunately, due to the limitation of the tensor-to-scalar ratio r , recent Planck + BICEP/Keck observations have ruled out the NI model [20,49].”
BackgroundMethodInfluential
SPT-3G+: mapping the high-frequency cosmic microwave background using kinetic inductance detectors
Anderson, A. J., Barry, P. S., Bender, A. N., et al. (2022) · Millimeter, Submillimeter, and Far-Infrared Detectors and Instrumentation for Astronomy XI · doi:10.1117/12.2629755 · Cited by 13
Self-citation
On Warm Natural Inflation and Planck 2018 Constraints
AlHallak, M., Said, K. K. A., Chamoun, N., & El‐Daher, M. S. (2023) · Universe · doi:10.3390/universe9020080 · Cited by 13
Cosmological consequences of domain walls biased by quantum gravity
Gouttenoire, Y., King, S. F., Roshan, R., Wang, X., White, G., & Yamazaki, M. (2025) · Physical review. D/Physical review. D. · doi:10.1103/7zmx-v16z · Cited by 25
Probing the supersymmetry-mass scale with F -term hybrid inflation
Lazarides, G., & Pallis, C. (2023) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.108.095055 · Cited by 12
Inflaton Decay in No-Scale Supergravity and Starobinsky-like Models
Ema, Y., García, M. A. G., Ke, W., Olive, K. A., & Verner, S. (2024) · Universe · doi:10.3390/universe10060239 · Cited by 14
Testing α -attractor quintessential inflation against CMB and low-redshift data
Giarè, W., Valentino, E. D., Linder, E. V., & Specogna, E. (2024) · Physics of the Dark Universe · doi:10.1016/j.dark.2024.101713 · Cited by 12
Exploring primordial black holes and gravitational waves with R-symmetric GUT Higgs inflation
Ijaz, N., & Rehman, M. U. (2024) · Physics Letters B · doi:10.1016/j.physletb.2024.139229 · Cited by 23
ξ-attractors in metric-affine gravity
Racioppi, A. (2025) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2025/04/084 · Cited by 12
“On the other hand, compatibility with experimental data [5] at 1 σ level, is already possible for ˜ f 0 = 4 and ˜ ξ ≃ 6 , 1 .”
Influential
Axion stabilization in modular cosmology
Carrasco, J. J. M., Каллош, Р., Linde, A. D., et al. (2025) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2025/07/090 · Cited by 12
“These predictions provide a good fit to the Planck/BICEP/Keck constraints on n s and r [20].”
The linear regime of tachyonic preheating
Koivunen, N., Tomberg, E., & Veermäe, H. (2022) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2022/07/028 · Cited by 12
Scalar induced gravitational waves from warm inflation
Arya, R., & Mishra, A. K. (2022) · Physics of the Dark Universe · doi:10.1016/j.dark.2022.101116 · Cited by 12
A hybrid map-C ℓ component separation method for primordial CMB B-mode searches
Azzoni, S., Alonso, D., Abitbol, M. H., et al. (2023) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2023/03/035 · Cited by 12
“The simplest way to account for this is by allowing for a simple scale-independent frequency decorrelation parameter, as would be the case for uncorrelated spatial variations [15, 17].”
Background
Primordial Black Holes from Volkov–Akulov–Starobinsky Supergravity
Aldabergenov, Y., & Ketov, S. V. (2023) · Fortschritte der Physik · doi:10.1002/prop.202300039 · Cited by 12
“As for the tensor-to-scalar ratio r, it tends to larger values with increasing a0, though still within the current CMB bounds [34, 35].”
Background
Loop Quantum Cosmology: Relation Between Theory and Observations
Agulló, I., Wang, A., & Wilson-Ewing, E. (2023) · Springer eBooks · doi:10.1007/978-981-19-3079-9_103-1 · Cited by 12
The Quantum Gravity Connection between Inflation and Quintessence
Wetterich, C. (2022) · Galaxies · doi:10.3390/galaxies10020050 · Cited by 13
“036 [62] implies σN > 885, while 1−n ≈ 0.”
Baryogenesis from combined Higgs–scalar field inflation
Cado, Y., & Mariano Quirós, C. (2022) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.106.055018 · Cited by 12
“where we have included, in the last r determination, the most recent combined result from the BICEP/Keck collaboration [50].”
Method
Issues in Palatini R2 inflation: Bounds on the reheating temperature
Lahanas, A. B. (2022) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.106.123530 · Cited by 12
“036 put by BICEP/Keck observations [84].”
Background
SPT-3G D1: Constraints on inflationary gravitational waves with two years of SPT-3G data
Zebrowski, J. A., Reichardt, C. L., Anderson, A. J., et al. (2025) · Physical review. D/Physical review. D. · doi:10.1103/33wm-c6pt · Cited by 11
Self-citation
QUBIC III: Laboratory characterization
Torchinsky, S. A., Hamilton, J. –., Piat, M., Battistelli, E. S., de Bernardis, P., Chapron, C., D’Alessandro, G., Petris, M. D., Lerena, M. M. G., González, M., et al. (2022) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2022/04/036 · Cited by 11
Self-citation
Non-minimally coupled Natural Inflation: Palatini and Metric formalism with the recent BICEP/Keck
Bostan, N. (2023) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2023/02/063 · Cited by 11
Quantum Gravity and Scale Symmetry in Cosmology
WETTERICH, C. (2023) · Springer eBooks · doi:10.1007/978-981-19-3079-9_26-1 · Cited by 16
A small Universe
Lehners, J.-L., & Quintin, J. (2024) · Physics Letters B · doi:10.1016/j.physletb.2024.138488 · Cited by 19
“Figure 5: A plot of the predictions of the natural inflation models considered here with various parameter values f and compared to the observational bounds obtained by the Planck satellite [32] (in green) and the BICEP/Keck experiments [40] (in blue).”
Landscape, Swampland and extra dimensions
Ignatios Antoniadis, A., Anchordoqui, L. A., & Lüst, D. (2024) · Corfu Summer Institute School and Workshops on Elementary Particle Physics and Gravity (CORFU) · doi:10.22323/1.463.0215 · Cited by 14
Robust constraints on tensor perturbations from cosmological data: A comparative analysis from Bayesian and frequentist perspectives
Galloni, G., Versillé, S., & Tristram, M. (2024) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.110.063511 · Cited by 11
Modular invariant slow roll inflation
Ding, G.-J., Jiang, S.-Y., & Zhao, W. (2024) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2024/10/016 · Cited by 11
“The current bounds on the spectral index and tensor-to-scalar ratio are important for constraining inflationary models: [2, 30]: ln (10 10 A s ) = 3 .”
Background
Geometrical origin of inflation in Weyl-invariant Einstein-Cartan gravity
Karananas, G. K. (2025) · Physics Letters B · doi:10.1016/j.physletb.2025.139343 · Cited by 11
A universal constraint on axion non-Abelian dynamics during inflation
Dimastrogiovanni, E., Fasiello, M., Michelotti, M., et al. (2025) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2025/03/007 · Cited by 11
“Several single-field models such as Higgs [2] and Starobinsky [3] inflation, fiber inflation [4], as well α -attractors [5] 1 remain in excellent agreement with CMB observations [6, 7].”
Ultraslow-roll inflation on the lattice. II. Nonperturbative curvature perturbation
Caravano, A., Franciolini, G., & Renaux‐Petel, S. (2025) · Physical review. D/Physical review. D. · doi:10.1103/39qd-gdfm · Cited by 11
Efficient ILC analysis on polarization maps after EB leakage correction
Zhang, Z., Liu, Y., Li, S., et al. (2022) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2022/07/044 · Cited by 11
Detectability of the Cross-Correlation between CMB Lensing and Stochastic GW Background from Compact Object Mergers
Capurri, G., Lapi, A., & Baccigalupi, C. (2022) · Universe · doi:10.3390/universe8030160 · Cited by 11
The rise of the primordial tensor spectrum from an early scalar-tensor epoch
Chowdhury, D., Gianmassimo Tasinato, C., & Ivonne Zavala, C. (2022) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2022/08/010 · Cited by 11
Primordial non-Guassianity in inflation with gravitationally enhanced friction
Chen, L., Yu, H., & Wu, P. (2022) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.106.063537 · Cited by 11
Circumventing the challenges in the choice of the nonconformal coupling function in inflationary magnetogenesis
Tripathy, S., Chowdhury, D., Ragavendra, H. V., et al. (2023) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.107.043501 · Cited by 11
Characterizing the post-inflationary reheating history. Part II. Multiple interacting daughter fields
Antusch, S., Marschall, K., & Torrentí, F. (2023) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2023/02/019 · Cited by 11
Production of Primordial Black Holes in Improved E-Models of Inflation
Frolovsky, D., & Ketov, S. V. (2023) · Universe · doi:10.3390/universe9060294 · Cited by 16
Parker bounds on monopoles with arbitrary charge from galactic and primordial magnetic fields
Kobayashi, T., & Perri, D. (2023) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.108.083005 · Cited by 11
“…that the velocity transition happens during the reheating epoch, and in particular after the primordial magnetic fields are generated, hence Here H inf is the inflationary Hubble rate, which is constrained by current observational limits on primordial gravitational waves as [51] H inf ≲ 10 14 GeV .”
Background
Bimetric Starobinsky model
Gialamas, I. D., & Tamvakis, K. (2023) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.108.104023 · Cited by 11
Unification: Emergent universe followed by inflation and dark epochs from multi-field theory
Guendelman, E. I., & Herrera, R. (2023) · Annals of Physics · doi:10.1016/j.aop.2023.169566 · Cited by 18
Ultraviolet freeze-in dark matter through the dilaton portal
Ahmed, A., & Najjari, S. (2023) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.107.055020 · Cited by 11
“For the slow-roll inflationary scenario the recent Planck [55] and BICEP/Keck [56] measurements put an upper bound at 95% C.”
BackgroundInfluential
Deformations of Starobinsky inflation in no-scale SU(5) and SO(10) GUTs
Ellis, J. R., García, M. A. G., Nagata, N., Nanopoulos, D. V., & Olive, K. A. (2025) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2025/12/038 · Cited by 24
CLASS Data Pipeline and Maps for 40 GHz Observations through 2022
Li, Y., Eimer, J. R., Osumi, K., et al. (2023) · The Astrophysical Journal · doi:10.3847/1538-4357/acf293 · Cited by 10
Self-citation
CMB imprints of high scale non-thermal leptogenesis
Ghoshal, A., Nanda, D., & Saha, A. K. (2024) · Physics Letters B · doi:10.1016/j.physletb.2024.138484 · Cited by 10
Challenges to Inflation in the Post-Planck Era
Liu, J., & Melia, F. (2024) · The Astrophysical Journal · doi:10.3847/1538-4357/ad4036 · Cited by 10
Natural inflation with exponentially small tensor-to-scalar ratio
Lorenzoni, D. L., Kaiser, D. I., & McDonough, E. (2024) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.110.l061302 · Cited by 19
“036 [27].”
Detection prospects of gravitational waves from SU(2) axion inflation
Badger, C., Duval, H., Fujita, T., Kuroyanagi, S., Romero, A., & Sakellariadou, M. (2024) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.110.084063 · Cited by 11
“036 at 95% CL [47].”
Electroweak metastability and Higgs inflation
Masina, I., & Mariano Quirós, C. (2024) · The European Physical Journal C · doi:10.1140/epjc/s10052-024-13522-x · Cited by 10
“The constraint on the inflationary potential is thus The most recent analysis of the BICEP, Keck Array and Planck data [53] places an upper bound on the tensor-to-scalar ratio r 0 .”
CMB constraints on natural inflation with gauge field production
Alam, K., Dutta, K., & Jaman, N. (2024) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2024/12/015 · Cited by 10
“We also show 2-σ allowed contours for 2018 Planck TT, TE, EE+lowE+lensing [1] (henceforth will be mentioned as Planck18) and 1-σ and 2-σ contours for 2018 Planck TT, TE, EE+lowE+lensing+BK18+BAO [13] (henceforth will be called Planck18+BK18).”
Influential
Primordial black holes and scalar-induced gravitational waves in sneutrino hybrid inflation
Afzal, A., Ghoshal, A., & King, S. F. (2025) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.111.023050 · Cited by 11
“The solid contours are the current Planck bounds [26], Planck/BICEP [25, 27, 28] and the dashed shaded region indicates the future proposed experiments (LiteBIRD, CMB-Euclid, Simons Observatory (SO)) [29–31].”
BICEP/ Keck XVIII: Measurement of BICEP3 polarization angles and consequences for constraining cosmic birefringence and inflation
Ade, P. A. R., Ahmed, Z., Amiri, M., Barkats, D., Thakur, R. B., Bischoff, C. A., Beck, D., Bock, J. J., Boenish, H., Buza, V., et al. (2025) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.111.063505 · Cited by 16
Self-citation
Dark matter ultraviolet freeze-in in general reheating scenarios
Bernal, N., Deka, K., & Losada, M. (2025) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.111.055034 · Cited by 10
“0 × 10 − 5 M P [81].”
General Einstein-Cartan quadratic gravity with derivative couplings
Katsoulas, T., & Tamvakis, K. (2025) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2025/06/022 · Cited by 10
“The existing observations of CMB [142, 143], corresponding to the Planck, BICER/Keck and BAO data, constrain the observables at the pivot scale k ⋆ = 0 .”
Influential
Towards a complete treatment of scalar-induced gravitational waves with early matter domination
Kumar, S., Tai, H., & Wang, L.-T. (2025) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2025/07/089 · Cited by 10
“We also fix H = 4 × 10 13 GeV, slightly below the current upper limit [87] and target of future B-mode experiments, ρ end ≃ V k / 100 (see, e.g., [84–86]), and a reheat temperature after inflation T RH = 10 The result is shown in Fig.”
Universal Bound on the Duration of a Kination Era
Eröncel, C., Gouttenoire, Y., Sato, R., Servant, G., & Simakachorn, P. (2025) · Physical Review Letters · doi:10.1103/k7ty-gwjg · Cited by 20
Pure chromo-natural inflation: signatures of particle production from weak to strong backreaction
Dimastrogiovanni, E., Fasiello, M., Papageorgiou, A., et al. (2025) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2025/09/042 · Cited by 10
Instability of the electroweak vacuum in Starobinsky inflation
Li, Q., Moroi, T., Nakayama, K., & Yin, W. (2022) · Journal of High Energy Physics · doi:10.1007/jhep09(2022)102 · Cited by 10
Quantum gravitational signatures in next-generation gravitational wave detectors
Das, S., Shankaranarayanan, S., & Todorinov, V. (2022) · Physics Letters B · doi:10.1016/j.physletb.2022.137511 · Cited by 10
QUIJOTE scientific results – VII. Galactic AME sources in the QUIJOTE-MFI northern hemisphere wide survey
Poidevin, F., Génova-Santos, R., Rubiño-Martín, J. A., et al. (2023) · Monthly Notices of the Royal Astronomical Society · doi:10.1093/mnras/stac3151 · Cited by 10
Revisiting f(R) gravity's rainbow: Inflation and primordial fluctuations
Leyva, Y., & Otalora, G. (2023) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2023/04/030 · Cited by 10
Primordial stochastic gravitational wave backgrounds from a sharp feature in three-field inflation. Part I. The radiation era
Aragam, V., Paban, S., & Rosati, R. (2023) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2023/11/014 · Cited by 10
“Furthermore, inﬂationary dynamics do not easily permit these tensor modes to have a strong scale dependence, since they are closely proportional”
Background
Invisible low-frequency gravitons and the audio band
Massimo Giovannini, A. (2023) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.108.123508 · Cited by 10
Beyond (and back to) Palatini quadratic gravity and inflation
Dioguardi, C., Racioppi, A., & Tomberg, E. (2024) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2024/03/041 · Cited by 10
“We found that the steeper the potential, the better the agreement with the experimental constraints [64], with the negative exponential potential the most favoured of all the cases considered.”
BackgroundMethodInfluential
Induced gravitational waves and baryon asymmetry fluctuations from primordial black hole formation
Altavista, C., & Rey, J. (2024) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2024/04/052 · Cited by 10
“01 [48, 49] and G♭ NLO = 2/3 for simplicity,”
Background
Improving constraints on inflation with CMB delensing
Trendafilova, C., Hotinli, S. C., & Meyers, J. (2024) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2024/06/017 · Cited by 10
“036 at the 95% confidence level [69, 70].”
Constraining ultra slow roll inflation using cosmological datasets
Ragavendra, H. V., Sarkar, A. K., & Sethi, S. K. (2024) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2024/07/088 · Cited by 10
Dark matter production in Weyl R2 inflation
Wang, Q.-Y., Tang, Y., & Wu, Y.-L. (2022) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.106.023502 · Cited by 10
Inflation with massive spin-2 ghosts
Kubo, J., Kuntz, J., Rezacek, J., et al. (2022) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2022/11/049 · Cited by 10
Ultraviolet sensitivity in Higgs-Starobinsky inflation
Lee, S. M., Modak, T., Oda, K.-Y., & Takahashi, T. (2023) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2023/08/045 · Cited by 10
Lectures on classical and quantum cosmology
Calcagni, G., Luca, M. G. D., & Fodran, T. (2022) · Corfu Summer Institute School and Workshops on Elementary Particle Physics and Gravity (CORFU) · doi:10.22323/1.406.0317 · Cited by 10
(Super)universal attractors and the de Sitter vacua in string landscape
Güleryüz, Ö. (2023) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2023/05/039 · Cited by 9
Delensing of Cosmic Microwave Background Polarization with Machine Learning
Yan, Y.-P., Wang, G.-J., Li, S., et al. (2023) · The Astrophysical Journal Supplement Series · doi:10.3847/1538-4365/acd2ce · Cited by 9
Reconstructing inflation and reheating in f ( ϕ ) T gravity
Herrera, R., & Ríos, C. (2023) · Annals of Physics · doi:10.1016/j.aop.2023.169484 · Cited by 9
Minimal solution to the axion isocurvature problem from nonminimal coupling
Berbig, M. (2024) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.110.095008 · Cited by 12
“036 [36].”
Analytic and numerical study of scalar perturbations in loop quantum cosmology
Marugán, G. A. M., Vicente-Becerril, A., & Carrilero, J. Y. (2024) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.110.043508 · Cited by 9
Analysis of Polarized Dust Emission Using Data from the First Flight of SPIDER
Ade, P. A. R., Amiri, M., Benton, S. J., Bergman, A. S., Bihary, R., Bock, J. J., Bond, J. R., Bonetti, J. A., Bryan, S., Chiang, H. C., et al. (2025) · The Astrophysical Journal · doi:10.3847/1538-4357/ad900c · Cited by 9
Self-citation
Stochastic axionlike curvaton: Non-Gaussianity and primordial black holes without a large power spectrum
Chen, C., Ghoshal, A., Gianmassimo Tasinato, C., & Tomberg, E. (2025) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.111.063539 · Cited by 9
“1 × 10 − 9 [143, 144] imply Solving Eq.”
Updating GUT-scale pole Higgs inflation after ACT DR6
Pallis, C. (2025) · Physical review. D/Physical review. D. · doi:10.1103/h1p2-c333 · Cited by 9
Bouncing cosmological isotropic solutions in scalar-tensor gravity
Polarski, D., Starobinsky, A. A., & Verbin, Y. (2022) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2022/01/052 · Cited by 9
“And indeed, a narrow subclass of inflationary models, the simplest of them depending on one free parameter to be fixed by observations only, quantitatively predicted the form of the observed spectrum of primordial scalar (matter density) inhomogeneities in the Universe at large scales, while many other models have bee…”
Background
Single-field slow-roll effective potential from Kähler moduli stabilizations in type-IIB/F-theory
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Leading all-loop quantum contribution to the effective potential in the inflationary cosmology
Kazakov, D. I., Iakhibbaev, R. M., & Tolkachev, D. M. (2023) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2023/09/049 · Cited by 9
“According to the relic radiation data obtained from the BICEP/PLANCK [15, 16], the observed values for these quantities are as follows:”
MethodInfluential
Impact of Galactic dust non-Gaussianity on searches for B-modes from inflation
Abril-Cabezas, I., Hervías-Caimapo, C., von Hausegger, S., Sherwin, B. D., & Alonso, D. (2023) · Monthly Notices of the Royal Astronomical Society · doi:10.1093/mnras/stad3529 · Cited by 9
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Reheating constraints on mutated hilltop inflation
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Introduction to the Number of e-Folds in Slow-Roll Inflation
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“036 at 95% CL [98].”

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

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