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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 201–300 of 1,009

Constraining burdened PBHs with gravitational waves
Barman, B., Loho, K., & Zapata, Ó. (2024) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2024/10/065 · Cited by 20
Warm Inflation with the Standard Model
Berghaus, K. V., Drewes, M., & Zell, S. (2025) · Physical Review Letters · doi:10.1103/9nn9-bsm9 · Cited by 35
Lattice simulations of non-minimally coupled scalar fields in the Jordan frame
Figueroa, D. G., Florio, A., Opferkuch, T., & Stefanek, B. A. (2023) · SciPost Physics · doi:10.21468/scipostphys.15.3.077 · Cited by 36
“Scenarios where the inflaton has a non-minimal gravitational coupling ξ|φ|2R lead to inflationary predictions in excellent agreement with current observational constraints [21, 22].”
Is cosmic birefringence model-dependent?
Yin, L., Kochappan, J. P., Ghosh, T., & Lee, B.-H. (2023) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2023/10/007 · Cited by 20
LiteBIRD science goals and forecasts: improving sensitivity to inflationary gravitational waves with multitracer delensing
Namikawa, T., Lonappan, A. I., Baccigalupi, C., et al. (2024) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2024/06/010 · Cited by 20
Self-citation
Inflation in Weyl-invariant Einstein-Cartan gravity
Gialamas, I. D., & Tamvakis, K. (2025) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.111.044007 · Cited by 20
“Regarding the cosmological observables constrained by recent observations [91, 92], we start with the amplitude of the primordial curvature perturbation on super-Hubble scales produced by single-field slow-roll inflation.”
Influential
On the number of e-folds in the Jordan and Einstein frames
Racioppi, A., & Vasar, M. (2022) · The European Physical Journal Plus · doi:10.1140/epjp/s13360-022-02853-x · Cited by 20
“The gray areas represent the 1, 2σ allowed regions from the latest combination of Planck, BICEP/Keck and BAO data [5]”
MethodInfluential
Inflation in F ( R ) gravity models revisited after ACT
Ketov, S. V., Pozdeeva, E. O., & Vernov, S. Y. (2025) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2025/12/040 · Cited by 19
“The CMB measurements by Planck/BICEP Collaborations [2] and Atacama Cosmology Telescope (ACT) [21, 22] combined with DESI 2024 data [23] are discussed in section 7.”
Influential
Circularly polarized scalar induced gravitational waves from the Chern-Simons modified gravity
Zhang, F., Feng, J.-X., & Gao, X. (2022) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2022/10/054 · Cited by 19
“Although a variety of information in understanding the early universe and fundamental physics is encoded in the primordial GWs, the primordial GWs have not been detected on the cosmic microwave background (CMB) scale up to now [11, 12].”
Background
Unifying inflation with early and late dark energy with multiple fields: Spontaneously broken scale invariant two measures theory
Guendelman, E. I., Herrera, R., & Benisty, D. (2022) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.105.124035 · Cited by 29
BICEP/Keck. XVI. Characterizing Dust Polarization through Correlations with Neutral Hydrogen
Ade, P. A. R., Ahmed, Z., Amiri, M., et al. (2023) · The Astrophysical Journal · doi:10.3847/1538-4357/acb64c · Cited by 19
Self-citation
Large field polynomial inflation: parameter space, predictions and (double) eternal nature
Drees, M., & Xu, Y. (2022) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2022/12/005 · Cited by 23
Relic gravitons and high-frequency detectors
Massimo Giovannini, A. (2023) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2023/05/056 · Cited by 19
Kontsevich-Segal Criterion in the No-Boundary State Constrains Inflation
Hertog, T., Janssen, O., & Karlsson, J. (2023) · Physical Review Letters · doi:10.1103/physrevlett.131.191501 · Cited by 30
“Superposed on these theoretical predictions are the observational constraints following from the 2018 Planck TT,TE,EE+lowE+lensing analysis [30] ( 68% and 95% confidence levels), indicated in purple, and, in blue, the constraints with the combined 2018 BICEP/Keck data and BAO added [33].”
Background
Scalar-induced gravitational waves from ghost inflation and parity violation
García-Sáenz, S., Lu, Y., & Shuai, Z. (2023) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.108.123507 · Cited by 19
“9 If we assume that T ζ is a polynomial in these two scalar quantities, and given that even powers of ( k · q 1 × q 2 ) are redundant, we then infer that only monomials containing even powers of ( q 1 · q 2 ) can in principle yield a net non-zero contribution.”
Background
Non-oscillating early dark energy and quintessence from α-attractors
Brissenden, L., Dimopoulos, K., & López, S. S. (2023) · Astroparticle physics · doi:10.1016/j.astropartphys.2024.102925 · Cited by 14
Gauge preheating with full general relativity
Adshead, P. J., Giblin, J. T., Grutkoski, R., et al. (2024) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2024/03/017 · Cited by 19
“We consider a simple toy model of inflation specified by the potential [2] Though inflation driven by a monomial potential is strongly disfavored [86, 87], we choose a quadratic potential merely to provide a simple model for the inflaton’s dynamics during preheating.”
Method
Natural metric-affine inflation
Racioppi, A., & Salvio, A. (2024) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2024/06/033 · Cited by 19
“4 we plot the corresponding results for r and n s versus the parameters ξ and δ f when N e = 60 and δ Λ is fixed so that the constraint (4.7) is satisfied.”
Influential
Primordial Black Holes in Scalar Field Inflation Coupled to the Gauss–Bonnet Term with Fractional Power-law Potentials
Ashrafzadeh, A., & Karami, K. (2024) · The Astrophysical Journal · doi:10.3847/1538-4357/ad293f · Cited by 21
Planck constraints on cosmic birefringence and its cross-correlation with the CMB
Zagatti, G., Bortolami, M., GRUPPUSO, A., et al. (2024) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2024/05/034 · Cited by 19
“BICEP2/Keck Array [8] and SPT [24].”
Resonant reheating
Barman, B., Bernal, N., & Xu, Y. (2024) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2024/08/014 · Cited by 19
“036 [69], we set n T = 0 throughout our which corresponds to a scale-invariant primordial spectrum.”
Background
In-flight polarization angle calibration for LiteBIRD: blind challenge and cosmological implications
Krachmalnicoff, N., Matsumura, T., de la Hoz, E., Basak, S., GRUPPUSO, A., Minami, Y., Baccigalupi, C., Komatsu, E., Martínez-González, E., Vielva, P., et al. (2022) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2022/01/039 · Cited by 19
Viability of warm inflation with standard model interactions
Ramos, R. O., & Rodrigues, G. S. (2025) · Physical review. D/Physical review. D. · doi:10.1103/wn1m-19gt · Cited by 18
Confronting rainbow-deformed f ( R ) gravity with the ACT data
Odintsov, S. D., & Oikonomou, V. K. (2025) · Physics Letters B · doi:10.1016/j.physletb.2025.139909 · Cited by 18
BEYONDPLANCK
Svalheim, T. L., Zonca, A., Andersen, K. J., Aurlien, R., Banerji, R., Bersanelli, M., Bertocco, S., Brilenkov, M., Carbone, M., Colombo, L. P. L., et al. (2022) · Astronomy and Astrophysics · doi:10.1051/0004-6361/202243080 · Cited by 18
Simple single-field inflation models with arbitrarily small tensor/scalar ratio
Stein, N. K., & Kinney, W. H. (2023) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2023/03/027 · Cited by 18
Bouncing cosmology in VCDM
Ganz, A., MARTENS, P. M., Shinji Mukohyama, A., & Namba, R. (2023) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2023/04/060 · Cited by 18
Flavor leptogenesis during the reheating era
Datta, A., Roshan, R., & Sil, A. (2023) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.108.035029 · Cited by 18
Cosmological probes of grand unification: Primordial black holes and scalar-induced gravitational waves
Ghoshal, A., Moursy, A., & Qaisar Shafi, A. (2023) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.108.055039 · Cited by 18
Starting inflation from inhomogeneous initial conditions with momentum
Corman, M., & East, W. E. (2023) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2023/10/046 · Cited by 18
“…the simplest models of inflation (including the quadratic potential we study here), are now strongly disfavored by the most recent observations from BICEP/Keck and Planck [10, 11], they could still appear in the context of more complicated inflationary models containing more than one scalar field.”
BackgroundResultInfluential
Dark energy, D-branes and pulsar timing arrays
Chowdhury, D., Gianmassimo Tasinato, C., & Ivonne Zavala, C. (2023) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2023/11/090 · Cited by 18
“036 provided by the BICEP/Keck collaboration [50].”
Reconciling early dark energy with a Harrison-Zeldovich spectrum
Fu, C., & Wang, S.-J. (2024) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.109.l041304 · Cited by 19
“The orange, purple, and blue shaded regions are the cosmological constraints [52] from the dataset Planck 2018 + BICEP/Keck + BAO + Pantheon for the ΛCDM model [49], AdS-EDE model [52], and ax-ionlike EDE model (with an equivalent H 0 prior) [13, 14], respectively.”
MethodResult
Relaxing inflation models with nonminimal coupling: A general study
Kodama, T., & Takahashi, T. (2022) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.105.063542 · Cited by 18
“As mentioned in the introduction, the minimally coupled version of chaotic inflation for any p has been excluded by the constraints on ns and r from Planck+BAO+BICEP/Keck 2018 [2].”
BackgroundResultInfluential
Approximate reconstruction of inflationary potential with ACT observations
Yi, Z., Wang, X., Gao, Q., et al. (2025) · Physics Letters B · doi:10.1016/j.physletb.2025.140002 · Cited by 17
Festina-Lente bound on Higgs vacuum structure and inflation
Lee, S. M., Cheong, D. Y., Hyun, S. C., Park, S. C., & Seo, M. (2022) · Journal of High Energy Physics · doi:10.1007/jhep02(2022)100 · Cited by 21
“which is much more stringent than the conventionally known bound HI < 1013−14 GeV from the recent Planck+BICEP/Keck 2018 observations [36].”
Background
Slow-roll inflation and reheating in Rastall theory
Afshar, B., Moradpour, H., & Shabani, H. (2023) · Physics of the Dark Universe · doi:10.1016/j.dark.2023.101357 · Cited by 17
Einstein-Proca theory from the Einstein-Cartan formulation
Barker, W., & Zell, S. (2024) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.109.024007 · Cited by 22
“Agreement with recent measurements, in particular of the cosmic microwave background (CMB) [13, 14], is excellent but a microscopic origin has still not been determined both for dark energy and for inflation.”
Background
Starobinsky inflation and beyond in Einstein-Cartan gravity
He, M., Hong, M., & Mukaida, K. (2024) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2024/05/107 · Cited by 17
“036 at 95% confidence [8].”
Background
LiteBIRD and CMB-S4 sensitivities to reheating in plateau models of inflation
Drewes, M., Lei, M., & Oldengott, I. M. (2024) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2024/05/081 · Cited by 18
“This choice of kp is also the standard convention of e.g. the Planck [107] and BICEP [87] collaborations.”
BackgroundMethodInfluential
Primordial gravitational wave backgrounds from phase transitions with next generation ground based detectors
Caprini, C., Pujolàs, O., Leclere, H. Q., Rompineve, F., & Steer, D. A. (2024) · Classical and Quantum Gravity · doi:10.1088/1361-6382/ad9a48 · Cited by 17
Primordial Black Holes Generated by Fast-roll Mechanism in Noncanonical Natural Inflation
Heydari, S., & Karami, K. (2024) · The Astrophysical Journal · doi:10.3847/1538-4357/ad7605 · Cited by 19
Primordial power spectrum at N3LO in effective theories of inflation
Eugenio Bianchi, A., & Gamonal, M. (2024) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.110.104032 · Cited by 17
“The constant Hubble rate H ( t ) = H ∗ results in a scale-invariant power spectrum P ∼ H 2 ∗ .”
Pseudo-Goldstone dark matter from primordial black holes: gravitational wave signatures and implications for KM3-230213A event at KM3NeT
Jiang, S., & Huang, F. P. (2025) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2025/06/023 · Cited by 18
“036 ， namely, the upper limit of Hubble scale during inflation H ( T in ) ≤ 5 × 10 13 GeV [69, 70].”
Fitting Power Spectrum of Scalar Perturbations for Primordial Black Hole Production during Inflation
Frolovsky, D., & Ketov, S. V. (2023) · Astronomy · doi:10.3390/astronomy2010005 · Cited by 23
Inflationary models with Gauss–Bonnet coupling in light of ACT observations
Zhu, Y., Gao, Q., Gong, Y., et al. (2025) · The European Physical Journal C · doi:10.1140/epjc/s10052-025-14969-2 · Cited by 16
“…satisfy To be consistent with the joint constraints on n s and r obtained from the P-ACT-LB dataset combined with the B-mode polarization measurements from the Background ImagingofCosmicExtragalacticPolarization(BICEP)/Keck Array experiments (BK18) [82], denoted as P-ACT-LB-BK18, we show in Fig.”
The early universe is ACT -ing warm
Berera, A., Brahma, S., Qiu, Z., et al. (2025) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2025/11/059 · Cited by 16
R 2 -Higgs inflation: R 3 contribution and preheating after ACT and SPT data
Modak, T. (2025) · Physical review. D/Physical review. D. · doi:10.1103/srpt-jd6s · Cited by 16
“Ongoing experiments [6, 7] are actively searching for this last missing piece which are believed to be engraved in the CMB B -mode polarization, with future missions proposed [8].”
Influential
Polarized Synchrotron Foreground Assessment for CMB Experiments
Weiland, J. L., Addison, G. E., Bennett, C. L., et al. (2022) · The Astrophysical Journal · doi:10.3847/1538-4357/ac83ab · Cited by 16
Self-citation
Slow-roll inflation in the Jordan frame
Karčiauskas, M., & Díaz, J. J. T. (2022) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.106.083526 · Cited by 16
Novel CMB constraints on the α parameter in alpha-attractor models
Iacconi, L., Fasiello, M., Väliviita, J., & Wands, D. (2023) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2023/10/015 · Cited by 24
“In this work we focus on current Planck [19, 20] and BICEP/Keck [21] data, see the resulting ns measurement (4.”
Method
Generalized hilltop inflation
Lillepalu, H. G., & Racioppi, A. (2023) · The European Physical Journal Plus · doi:10.1140/epjp/s13360-023-04512-1 · Cited by 16
“2, but only for the points that are inside the experimental constraints for r and ns [6].”
BackgroundMethodInfluential
CMB-S4 forecasts for constraints on f NL through μ -distortion anisotropy
Zegeye, D., Bianchini, F., Bond, J. R., et al. (2023) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.108.103536 · Cited by 16
Observable gravitational waves from hyperkination in Palatini gravity and beyond
López, S. S., Dimopoulos, K., Καράμ, Α., & Tomberg, E. (2023) · The European Physical Journal C · doi:10.1140/epjc/s10052-023-12332-x · Cited by 16
“Precision observations [15, 16] of the acoustic peaks in the CMB primordial temperature anisotropy have verified in spectacular detail the predictions of Cosmic Inflation, such that the rival paradigm for structure”
Background
The Simons Observatory: Combining cross-spectral foreground cleaning with multitracer B -mode delensing for improved constraints on inflation
Hertig, E., Wolz, K., Namikawa, T., et al. (2024) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.110.043532 · Cited by 16
“Within this framework, we demonstrate the equivalence of map-based and cross-spectral delensing and use it to motivate an optimized pixel-weighting scheme for power spectrum estimation.”
BackgroundMethodSelf-citation
Quantum Loop Corrections in the Modified Gravity Model of Starobinsky Inflation with Primordial Black Hole Production
Saburov, S., & Ketov, S. V. (2024) · Universe · doi:10.3390/universe10090354 · Cited by 16
“[2, 3] for a recent review), being in excellent agreement with the current cosmic microwave background (CMB) radiation measurements [4, 5, 6].”
Background
Explaining PTA results by metastable cosmic strings from SO(10) GUT
Antusch, S., Hinze, K., & Saad, S. (2024) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2024/10/007 · Cited by 16
“The Planck [92] and BICEP2-Keck [93] experiments provide a stringent bound on the tensor-to-scalar ratio, r 0 .”
Method
Constraining the history of reheating with the NANOGrav 15-year data
Maity, S., Bhaumik, N., Haque, M. R., Maity, D., & Sriramkumar, L. (2025) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2025/01/118 · Cited by 18
“05 Mpc − 1 .”
Influential
Toward primordial gravitational waves and n s = 1 in light of BICEP/Keck and DESI BAO data and the Hubble tension
Wang, H., Ye, G., Jiang, J.-Q., et al. (2025) · Physical review. D/Physical review. D. · doi:10.1103/w19x-trrq · Cited by 16
A Measurement of the Largest-scale CMB E-mode Polarization with CLASS
Li, Y., Eimer, J. R., Appel, J. W., Bennett, C. L., Brewer, M. K., Bruno, S. M., Bustos, R., Chan, Y. Y., Chuss, D. T., Cleary, J., et al. (2025) · The Astrophysical Journal · doi:10.3847/1538-4357/adc723 · Cited by 16
Self-citation
Constraining α-attractor models from reheating
Germán, G. (2022) · International Journal of Modern Physics D · doi:10.1142/s021827182250081x · Cited by 16
Running primordial perturbations: Inflationary dynamics and observational constraints
Easther, R., Bahr-Kalus, B., & Parkinson, D. (2022) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.106.l061301 · Cited by 16
Generation of gravitational waves in dynamical Chern-Simons gravity
Peng, Z.-Z., Zeng, Z.-M., Fu, C., & Guo, Z. (2022) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.106.124044 · Cited by 16
Constraining cosmic inflation with observations: Prospects for 2030
Bahr-Kalus, B., Parkinson, D., & Easther, R. (2023) · Monthly Notices of the Royal Astronomical Society · doi:10.1093/mnras/stad092 · Cited by 16
Tracking the multifield dynamics with cosmological data: a Monte Carlo approach
Giarè, W., Angelis, M. D., van de Bruck, C., & Valentino, E. D. (2023) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2023/12/014 · Cited by 16
“Additionally, we include the most recent CMB B-modes power spectrum likelihood cleaned from foreground contamination, as released by the Bicep/Keck Array X Collaboration [9].”
BackgroundMethodInfluential
Improved Model of Primordial Black Hole Formation after Starobinsky Inflation
Saburov, S., & Ketov, S. V. (2023) · Universe · doi:10.3390/universe9070323 · Cited by 16
“The tilt ns of scalar perturbations agrees within 1σ with the current CMB measurements [3, 4, 5], ns = 0.”
BackgroundMethod
WI2easy : warm inflation dynamics made easy
Rodrigues, G. S., & Ramos, R. O. (2025) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2025/09/014 · Cited by 15
Constraints on attractor models of inflation and reheating from P l a n c k , BICEP/Keck, ACT DR6, and SPT-3G data
Ellis, J. R., García, M. A. G., Olive, K. A., & Verner, S. (2026) · Physical review. D/Physical review. D. · doi:10.1103/d35r-7bn8 · Cited by 15
Pole inflation and primordial black holes formation in Starobinsky-like supergravity
Aoki, S., Ishikawa, R., & Ketov, S. V. (2023) · Classical and Quantum Gravity · doi:10.1088/1361-6382/acb884 · Cited by 15
“The improved precision measurements of the CMB radiation [5, 6] give for the spectral tilt n s of scalar perturbations the values The current observational upper bound [5, 6] on the CMB tensor-to-scalar ratio r is given by As is clear from table 1, the values of r in our model are well below the…”
Influential
Testing scale-invariant inflation against cosmological data
Cecchini, C., Angelis, M. D., Giarè, W., Rinaldi, M., & Vagnozzi, S. (2024) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2024/07/058 · Cited by 15
“…reconstruction likelihoods [258, 259], combined with the latest foreground-cleaned CMB B-mode power spectrum likelihood released by the BICEP/Keck collaboration, based on observations from the BICEP2 , Keck Array , and BICEP3 experiments up to and including the 2018 observation season [260].”
Method
Inflation and reheating in quadratic metric-affine gravity with derivative couplings
Gialamas, I. D., Katsoulas, T., & Tamvakis, K. (2024) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2024/06/005 · Cited by 15
“The shaded regions represent the permissible parameter space at confidence levels of 68% (dark blue) and 95% (light blue), as derived from the most recent combination of Planck, BICEP/Keck, and BAO data [132–135].”
Method
Primordial Black Holes with QCD Color Charge
Alonso-Monsalve, E., & Kaiser, D. I. (2024) · Physical Review Letters · doi:10.1103/physrevlett.132.231402 · Cited by 24
“Given that the Hawking temperature T H → 0 as a black hole approaches extremality, we actually expect t evap ≫ t QCD for near-extremal PBHs that form amid a plasma at T c = 5 × 10 7 GeV.”
Background
Quasi periodic oscillations around Kerr-type black hole in the Starobinsky–Bel–Robinson theory of gravity
Davlataliev, A., Narzilloev, B., Hussain, I., et al. (2024) · Physics of the Dark Universe · doi:10.1016/j.dark.2024.101569 · Cited by 15
First constraints on non-minimally coupled Natural and Coleman-Weinberg inflation and massive neutrino self-interactions with Planck+BICEP/Keck
Bostan, N., & Choudhury, S. R. (2024) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2024/07/032 · Cited by 15
“As far as the sensitivity of the current datasets is concerned (especially BICEP/Keck [7]), we find that introduction of neutrino self-interactions has negligible effects on the bounds on r 0 .”
BackgroundMethodInfluential
Primordial black holes and scalar-induced gravitational waves in radiative hybrid inflation
Afzal, A., & Ghoshal, A. (2024) · The European Physical Journal C · doi:10.1140/epjc/s10052-024-13246-y · Cited by 18
“The solid contours are the current Planck bounds [68], Planck/BICEP [1,50,69] and the dashed shaded region indicates the future proposed experiments (LiteBIRD, CMB S4-Euclid, Simons Observatory (SO)) [70–72] determines the number of e-folds in the waterfall regime and κ will ﬁx the amplitude of the…”
Revisiting the ultraviolet tail of the primordial gravitational wave
Pi, S., Sasaki, M., Wang, A., & Wang, J. (2024) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.110.103529 · Cited by 19
Novel primordial black hole production mechanism from non-Abelian gauge fields during inflation
Dimastrogiovanni, E., Fasiello, M., & Papageorgiou, A. (2024) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.110.103542 · Cited by 18
Chasing cosmic inflation: constraints for inflationary models and reheating insights
Ballardini, M. (2025) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2025/01/116 · Cited by 15
“We include B-mode polarisation spectrum for 20 ℓ 330 from BICEP2, Keck Array, and BICEP3 observations up to 2018 [47] (hereafter BK18).”
Inflationary and gravitational wave signatures of small primordial black holes as dark matter
Barker, W., Gladwyn, B. C., & Zell, S. (2025) · Physical review. D/Physical review. D. · doi:10.1103/4hrv-zfch · Cited by 15
Observable primordial gravitational waves from non-minimally coupled R 2 Palatini modified gravity
Kuralkar, H. J., Panda, S., & Vidyarthi, A. (2025) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2025/05/073 · Cited by 15
Impact of extragalactic foregrounds on internal delensing of the CMB B -mode polarization
Lizancos, A. B., & Ferraro, S. (2022) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.106.063534 · Cited by 15
Natural Inflation with non minimal coupling to gravity in R 2 gravity under the Palatini formalism
AlHallak, M., Chamoun, N., & El‐Daher, M. S. (2022) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2022/10/001 · Cited by 15
“However, a more recent analysis of BICEP/Keck XIII in 2018 (BK18) [4] has put more stringent bounds on r, so we included in our observational data those of Planck2018 (TT, EE, TE), BK18 and other experiments (lowE, lensing) separately or combined.”
MethodInfluential
Inflation from a generalized exponential plateau: towards extra suppressed tensor-to-scalar ratios
Kouniatalis, G., & Saridakis, E. N. (2025) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2025/11/038 · Cited by 14
“Perhaps most constraining, however, is the tensor-to-scalar ratio r , which quantifies the relative contribution of primordial gravitational waves to the CMB. Current observations from Planck and BICEP/Keck Array [11, 12] place a stringent upper bound r 0 .”
Effects of radiative corrections on Starobinsky inflation
Ellis, J. R., Tony Gherghetta, A., Kaneta, K., Ke, W., & Olive, K. A. (2025) · Physical review. D/Physical review. D. · doi:10.1103/8cx9-c642 · Cited by 22
Impact of half-wave plate systematics on the measurement of cosmic birefringence from CMB polarization
Monelli, M., Komatsu, E., Adler, A., Billi, M., Campeti, P., Dachlythra, N., Duivenvoorden, A. J., Gudmundsson, J. E., & Reinecke, M. (2023) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2023/03/034 · Cited by 14
Dissipative inflation via scalar production
Creminelli, P., Kumar, S., Salehian, B., et al. (2023) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2023/08/076 · Cited by 14
Warm inflation in f(R,T) gravity
Yeasmin, S., Deb, B., & Deshamukhya, A. (2023) · Chinese Journal of Physics · doi:10.1016/j.cjph.2023.07.004 · Cited by 14
Machine learning cosmic inflation
Kamerkar, A., Nesseris, S., & Pinol, L. (2023) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.108.043509 · Cited by 14
Impact of the damping tail on neutrino mass constraints
Valentino, E. D., Gariazzo, S., Giarè, W., & Mena, O. (2023) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.108.083509 · Cited by 14
Reheating constraints and consistency relations of the Starobinsky model and some of its generalizations
García, M. A. G., Germán, G., Quaglia, R. G., & Colorado, A. M. M. (2023) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2023/12/015 · Cited by 14
CLASS Angular Power Spectra and Map-component Analysis for 40 GHz Observations through 2022
Eimer, J. R., Li, Y., Brewer, M. K., Shi, R., Ali, A., Appel, J. W., Bennett, C. L., Bruno, S. M., Bustos, R., Chuss, D. T., et al. (2024) · The Astrophysical Journal · doi:10.3847/1538-4357/ad1abf · Cited by 14
Self-citation
Palatini F ( R , X ) : A new framework for inflationary attractors
Dioguardi, C., & Racioppi, A. (2024) · Physics of the Dark Universe · doi:10.1016/j.dark.2024.101509 · Cited by 14
Primordial gravitational waves assisted by cosmological scalar perturbations
Yu, Y.-H., & Wang, S. (2024) · The European Physical Journal C · doi:10.1140/epjc/s10052-024-12937-w · Cited by 14
Traversing a kinetic pole during inflation: primordial black holes and gravitational waves
Ghoshal, A., & Струмиа, А. (2024) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2024/07/011 · Cited by 14
Connecting Cosmic Inflation to Particle Physics with LiteBIRD, CMB-S4, EUCLID, and SKA
Drewes, M., & Lei, M. (2024) · Physical Review Letters · doi:10.1103/physrevlett.133.031001 · Cited by 14
Formation and decay of oscillons after inflation in the presence of an external coupling. Part I. Lattice simulations
Shafi, M., Copeland, E. J., Mahbub, R., Mishra, S. S., & Basak, S. (2024) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2024/10/082 · Cited by 14
“…the subspace of the parameter space, { λ, g 2 } , leading to oscillon formation as well as to study their subsequent decay due to the presence of such simple external interactions; all the while ensuring that the inflationary predictions are consistent with the latest CMB constraints [15, 16, 18].”
MethodInfluential
Induced gravitational waves, metastable cosmic strings and primordial black holes in GUTs
Maji, R., Moursy, A., & Qaisar Shafi, A. (2025) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2025/01/106 · Cited by 14
“101) × 10 − 9 [46, 47].”
Symmetry-breaking inflation in non-minimal metric-affine gravity
Gialamas, I. D., & Racioppi, A. (2025) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2025/05/072 · Cited by 14
“The gray (green) areas represent the 1,2 σ allowed regions coming from the latest combination of Planck, BICEP/Keck and BAO data [45] (from Planck legacy data [47]). combination of Planck, BICEP/Keck and BAO data [45].”
Is the formation of primordial black holes from single-field inflation compatible with standard cosmology?
Allegrini, S., Grosso, L. D., Iovino, A. J., & Alfredo Urbano, A. (2025) · Physical review. D/Physical review. D. · doi:10.1103/9rr3-ltbt · Cited by 14
Are single-field models of inflation and PBHs production ruled out by ACT observations?
Frolovsky, D., & Ketov, S. V. (2025) · Modern Physics Letters A · doi:10.1142/s0217732325501822 · Cited by 14
“032 [49], so that | ∆ ϕ | ≲ 10 M Pl , i.e. the duration of inflation and the length of the slow-roll plateau cannot exceed 100 e-folds.”
PBH assisted search for QCD axion dark matter
Choi, G., & Schiappacasse, E. D. (2022) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2022/09/072 · Cited by 14
“, BICEP/Keck) [19], the Gibbons-Hawking temperature TI = HI/2π = MP √ Asr/8 is constrained to be TI .”
BackgroundInfluential

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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