Suppressing the impact of a high tensor-to-scalar ratio on the temperature anisotropies

Carlo R. Contaldi; Lorenzo Sorbo; Marco Peloso

REVIEW

Suppressing the impact of a high tensor-to-scalar ratio on the temperature anisotropies

Carlo R. Contaldi, Marco Peloso, Lorenzo Sorbo

Cosmology and Nongalactic Astrophysics · Submitted 18 Mar 2014 · 46 references

Pith's verdict: A sensible, well-executed 'what if r really is 0.2' paper whose central comparison survives, but whose AIC table has a factor-of-two slip in the exponent that inflates the headline preference.

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CitationCarlo R. Contaldi, Lorenzo Sorbo, Marco Peloso. "Suppressing the impact of a high tensor-to-scalar ratio on the temperature anisotropies." arXiv:1403.4596 (2014). https://pith.science/paper/IQ7OVJHA

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Editor's note

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Worth your time if you care about how r gets extracted from TT, but read Table 2 with a calculator open. The core result holds: a Starobinsky-type step in the inflaton slope, giving ~26% suppression of scalar power below k* ≈ 0.0015/Mpc, fits Planck+WP+BICEP2 better than a constant running by Δχ² ≈ 7.5 for one extra parameter, and the marginalized posteriors in Fig. 4 exclude no-suppression. That is a real, if modest, improvement, and the mechanism is more motivated than the α_s ≈ −0.02 that running requires. The appendix step-function check is the part I trust most: it reproduces the same Δχ² and consistent (k*, β_s) without the ringing, which tells you the gain isn't an artifact of Starobinsky's oscillations. Good, honest robustness work. Section 3 is also clean — the derivation from Eq. 3.3 through 3.4–3.5 showing a primordial ζh correlator drops out of C_ℓ is correct, and footnote 1 openly reverses their own earlier claim after refs. 33–34. That kind of self-correction is rare enough to be worth noting. Now the soft spots. First, Table 2's relative-likelihood column is exp(ΔAIC), not the exp(ΔAIC/2) that Eq. 2.5 defines — ln(2.45×10⁻⁵) = −10.617 exactly. Recomputing from Table 1 gives relative likelihoods of ~0.006 and ~0.062, so suppression beats running ~16:1, not ~385:1. The direction is unchanged; 'strongly favoured' and the abstract's 'considerably better' are oversold by an order of magnitude, and Δχ² = 7.5 is ~2.7σ, not decisive. Second, the MCMC pins every background and nuisance parameter at Planck best-fit values ('for simplicity', Section 2). I think this is probably harmless because the gain sits at ℓ = 20–30 where ω_b, ω_c, θ barely matter, but the paper asserts rather than shows it, and a chi-squared difference this small deserves the full run. Third, r = 0.18 is essentially the BICEP2 input coming back out, not an independent confirmation. None of this is fatal, and the dust caveats are acknowledged. Send it out. It's a competent, clearly written model-comparison paper from a chaotic few weeks, and the referee should ask for the corrected AIC column and a full-parameter run.

Referee report

Significance

The question is timely and the proposed mechanism is physically motivated and simple: a modest, slow-roll-preserving change in the potential slope, rather than a running far outside slow-roll expectations. The negative result of Section 3 is useful and is presented with appropriate credit to Refs. [33,34] for correcting an earlier version (footnote 1), which is good practice and worth noting explicitly. The paper is clearly written, the model is falsifiable (the predicted low-ℓ suppression and the ringing in P_s are testable with Planck polarization and future B-mode data), and the parameter constraints in Figure 4 are reported with marginalized errors. The main strengths are the physical transparency of the suppression model and the honest correction of the earlier anticorrelation claim; the main weakness is that the headline statistical comparison rests on a reduced-parameter MCMC and on an AIC table whose likelihood column appears to be miscomputed.

Major objections (2)

[Table 2 and Eq. (2.5)] The relative-likelihood column of Table 2 is inconsistent with Eq. (2.5). Eq. (2.5) defines L_AIC = exp[(AIC_min − AIC)/2], but the tabulated values equal exp(ΔAIC): ln(2.45×10⁻⁵) = −10.617 and ln(0.0026) = −5.95, matching the ΔAIC entries without the factor of 1/2. Recomputing from Table 1 (AIC = 2N_p + χ²) gives AIC_min − AIC = 10.234 for ΛCDM+tensor and 5.556 for running, so the correct relative likelihoods are approximately 0.006 and 0.062, not 2.45×10⁻⁵ and 0.0026. The suppression model is still preferred, but by roughly 16:1 over running rather than ~385:1. In addition, the tabulated ΔAIC values (−10.617, −5.939) do not reproduce the Table 1 χ² and N_p entries (which give −10.234 and −5.556), so the column needs to be recomputed from a single consistent set of numbers. The qualitative conclusion survives, but the phrases 'strongly favoured' (Section 2 and Conclusions) and 'considerably better' (abstract:s6) should be softened to match the corrected numbers.
[Section 2, MCMC setup] The MCMC holds all cosmological and nuisance parameters other than τ, n_s, ln(10¹⁰A), r, k*, and Δ fixed at the Planck 'base r' best-fit values, as stated explicitly ('for simplicity'). The headline Δχ² ≈ 7.5 is small enough that shifts in ω_b, ω_c, θ, or the nuisance parameters could move it appreciably, and the paper does not demonstrate that the shortcut is harmless. Because the improvement is concentrated at 20 < ℓ < 30 (Figure 1), where the background parameters matter little, the concern is probably subdominant, but this should be shown rather than asserted. Either report a run with the full parameter space varied, or quantify how much of the Δχ² comes from the 20 < ℓ < 30 range and argue explicitly that the fixed parameters cannot absorb it. A short table decomposing the χ² improvement by multipole band would settle the point.

Minor objections (7)

[Abstract (abstract:s6)] The phrase 'a sudden change of the speed of the inflaton (by about 14%)' is imprecise: Δ = 0.14 is the fractional change in the slope of the potential (C₊ − C₋)/C₊, not the speed. The speed change is second order in Δ. Rephrase to 'a change in the slope of the inflaton potential' to match Eq. (2.1) and the text of Section 2.
[Table 1 caption] The caption states that 'Only the case with suppressed scalar power can accommodate the observed amplitude of r ~ 0.2', but the r column lists r = 0.18 for all three models, including ΛCDM+tensor and running. Clarify that the point is about fit quality at r = 0.18, not about which models can accommodate that value.
[Section 2, marginalized constraints] The marginalized constraint Δ = 0.106⁺⁰·⁰⁹²₋₀.₀₁₃ sits noticeably below the best-fit Δ = 0.14, and the errors are strongly asymmetric. Explain the shift (presumably a volume effect in the posterior) and state whether the best-fit or the marginalized value should be quoted as the headline suppression amplitude.
[Appendix A] The step-function fit gives k* = (4.07⁺⁰·⁷⁰₋₂.₄₅)×10⁻³ Mpc⁻¹, versus (1.80⁺⁰·⁸⁶₋₀.₆₉)×10⁻³ Mpc⁻¹ for the Starobinsky model. Calling these 'consistent' is a stretch given that the central values differ by a factor of ~2.3; state the overlap of the intervals explicitly rather than asserting consistency.
[Section 3] The negative result is derived under the Sachs-Wolfe approximation and a scale-invariant scalar-tensor correlator of the form (3.3). State these assumptions in the conclusion of the section, and note that the off-diagonal C_{ℓmℓ'm'} of Eqs. (3.4)–(3.5) are in principle observable even though C_ℓ is not affected; this would make the negative result more useful.
[Figure 2] The ℓ labels near the x-axis ('ℓ ≈ 5', 'ℓ ≈ 200', 'ℓ ≈ 2000') are hard to read and their mapping to k is not explained in the caption. Add a sentence in the caption or a secondary axis making the k–ℓ correspondence explicit.
[Footnote 1] The note that Section 3 was modified after Refs. [33,34] is good practice. Consider moving the substance of the correction into the main text so that readers of the published version see it without consulting the footnote.

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The paper

The paper claims

A sudden 14% change in the inflaton's slope can suppress large-scale scalar power enough to fit a tensor-to-scalar ratio near 0.2 without a large running.

The reading

The paper asks whether the large tensor-to-scalar ratio reported by BICEP2, $r$ approximately 0.2, can be reconciled with the temperature anisotropies without invoking a running of the scalar spectral index much larger than slow roll predicts. Its proposal is that scalar power is suppressed at large scales by a sudden change in the slope of the inflaton potential, so the temperature spectrum loses power where tensors contribute most while the B-mode signal remains. Using a Starobinsky step model, the authors find a best fit with a 14% change in slope, about 26% suppression below $k_*$ approximately $0.0015$ per Mpc, and $r=0.18$; the effective $chi^2$ improves by about 7.5 over constant running at the cost of one parameter, and the AIC also prefers the suppression model. If this holds, a high-scale inflationary signal in B modes need not be accompanied by an exotic running. The paper also checks whether a scalar-tensor anticorrelation could do the same job and concludes that it cannot, because it changes off-diagonal correlations but not the temperature power spectrum.

What carries the argument

The load-bearing mechanism is the Starobinsky piecewise-linear potential, $V(varphi)=V_0+C_+(varphi-varphi_*)$ for $varphi$ greater than or equal to $varphi_*$ and $V(varphi)=V_0+C_-(varphi-varphi_*)$ for $varphi$ less than or equal to $varphi_*$ with $C_- < C_+$. Its scalar power spectrum has a large-scale plateau suppressed by $(1- Delta)^2$, a small ringing from the sharp transition, and the usual tilt at small scales; the paper fits the full template rather than a bare step. The fit uses modified CAMB and CosmoMC, adding $k_*$ and $Delta$ to a reduced parameter set. For the anticorrelation section, the machinery is a scale-invariant $langle zeta h_{ij} rangle$ correlator projected onto transverse-traceless modes; the induced $C_{ell m ell+2m}$ and $C_{ell m ell m}$ terms average to zero in $C_ell$.

Extended reading notes

Core claim

The central claim is that a step-like suppression of the primordial scalar power at large scales can fit the Planck temperature data, WMAP9 polarization, and BICEP2 better than a constant running spectral index while keeping $r$ approximately 0.2. In the Starobinsky model the inflaton rolls from a steeper to a shallower slope; modes that leave the horizon before the step have their power reduced by $(1- Delta)^2$, while modes after it are unchanged. With $tau$, $n_s$, $ln(10^{10}A)$, $r$, $k_*$, and $Delta$ free and the other parameters fixed, the best fit is $k_* = 0.0015$ per Mpc, $Delta = 0.14$ (about 26% suppression), and $r=0.18$, with effective $chi^2 = 9838.87$ versus $9846.43$ for constant running, a $Delta chi^2$ approximately 7.5 for one extra parameter. The paper also shows that a primordial scalar-tensor anticorrelation produces off-diagonal $C_{ell m ell' m'}$ but leaves $C_ell$ unchanged, so it cannot lower the TT spectrum used to bound $r$; the authors note that this conclusion was revised from an earlier version after [33,34].

Load-bearing premise

The reconciliation rests on the BICEP2 B-mode being primordial and on a model comparison in which every cosmological and nuisance parameter except $tau$, $n_s$, $ln(10^{10}A)$, $r$, $k_*$, and $Delta$ is held fixed at the Planck base-$r$ best fit.

Editorial extensions

If this is right

A confirmed $r$ approximately 0.2 would not force a running $alpha_s$ approximately $-0.02$; a step in the potential can absorb the tension while the inflaton stays in slow roll before and after the transition.
The preferred suppression is concrete: about 26% less scalar power below $k_*$ approximately $1.5$ times $10^{-3}$ per Mpc, corresponding to the largest observable scales and the low-$ell$ temperature points.
Because the tensor power is continuous across the step, the model keeps a B-mode signal at $r$ approximately 0.18 while lowering only the large-scale scalar TT contribution.
A scalar-tensor anticorrelation is ruled out as a route to lowering the TT bound on $r$, since it changes off-diagonal correlations but not $C_ell$.
A ringing-free step-function parametrization gives consistent $k_*$ and $beta_s$, so the fit does not depend on the oscillatory part of the Starobinsky template.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

Editorial extension: a full-parameter likelihood run is the obvious next check; if the $Delta chi^2$ advantage shrinks when Planck's background and nuisance parameters vary, the suppression case would rest on the AIC penalty rather than on the fit itself.
The step's ringing, though minor here, leaves a calculable oscillatory imprint in the TT spectrum around the transition; a dedicated search at low $ell$ could distinguish a sharp Starobinsky step from a smooth sound-speed suppression.
If dust cleaning lowers BICEP2's $r$ below about 0.1, the original tension disappears, but the same large-scale suppression could still be tested as an independent explanation of the low-$ell$ TT deficit.
The off-diagonal correlations induced by a scalar-tensor correlator are a possible target for statistical-anisotropy searches, even though they cannot lower the temperature power spectrum.

Original abstract

The BICEP2 collaboration has reported a strong B mode signal in the CMB polarization, which is well fit by a tensor-to-scalar ratio of r ~ 0.2. This is greater than the upper limit r < 0.11 obtained from the temperature anisotropies under the assumption of a constant scalar spectral index n_s. This discrepancy can be reduced once the statistical error and the contamination from polarized dust are accounted for. If however a large value for r will be confirmed, it will need to be reconciled with the temperature anisotropies data. The most advocated explanation involves a variation of n_s with scales (denoted as running) that has a magnitude significantly greater than the generic slow roll predictions. We instead study the possibility that the large scale temperature anisotropies are not enhanced because of a suppression of the scalar power at large scales. Such a situation can be achieved for instance by a sudden change of the speed of the inflaton (by about 14 %), and we show that it fits the temperature anisotropies and polarization data considerably better than a constant running (its chi^2 improves by ~ 7.5 over that of the constant running, at the cost of one more parameter). We also consider the possibility that the large scale temperature fluctuations are suppressed by an anti-correlation between tensor and scalar modes. Unfortunately, while such effect does affect the temperature fluctuations at large scales, it does not affect the temperature power spectrum and cannot, therefore, help in reconciling a large value of r with the limits from temperature fluctuations.

The compiled record

The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 7,067 input tokens, $0.0003 reported.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.47 · human participants 0.01 · controlled comparison 0.38 · randomized assignment 0.01 · states quantitative result 0.98 · compares with prior results 0.96 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v4. Results and the main claim are underlined; show every role.

The BICEP2 collaboration has reported a strong B mode signal in the CMB polarization, which is well fit by a tensor-to-scalar ratio of r ~ 0.2. This is greater than the upper limit r < 0.11 obtained from the temperature anisotropies under the assumption of a constant scalar spectral index n_s. This discrepancy can be reduced once the statistical error and the contamination from polarized dust are accounted for. If however a large value for r will be confirmed, it will need to be reconciled with the temperature anisotropies data. The most advocated explanation involves a variation of n_s with scales (denoted as running) that has a magnitude significantly greater than the generic slow roll predictions. We instead study the possibility that the large scale temperature anisotropies are not enhanced because of a suppression of the scalar power at large scales. Such a situation can be achieved for instance by a sudden change of the speed of the inflaton (by about 14 %), and we show that it fits the temperature anisotropies and polarization data considerably better than a constant running (its chi^2 improves by ~ 7.5 over that of the constant running, at the cost of one more parameter). We also consider the possibility that the large scale temperature fluctuations are suppressed by an anti-correlation between tensor and scalar modes. Unfortunately, while such effect does affect the temperature fluctuations at large scales, it does not affect the temperature power spectrum and cannot, therefore, help in reconciling a large value of r with the limits from temperature fluctuations.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	The BICEP2 collaboration has reported a strong B mode signal in the CMB polarization, which is well fit by a tensor-to-scalar ratio of r ~ 0.2.	background 1.00	0.04	0.03	asserted 0.99
s1	This is greater than the upper limit r < 0.11 obtained from the temperature anisotropies under the assumption of a constant scalar spectral index n_s.	background 0.94	0.08	0.03	asserted 1.00
s2	This discrepancy can be reduced once the statistical error and the contamination from polarized dust are accounted for.	background 0.85	0.12	0.04	asserted 0.75
s3	If however a large value for r will be confirmed, it will need to be reconciled with the temperature anisotropies data.	background 0.74	0.06	0.04	hedged possibility 0.68
s4	The most advocated explanation involves a variation of n_s with scales (denoted as running) that has a magnitude significantly greater than the generic slow roll predictions.	background 0.99	0.05	0.04	asserted 0.89
s5	We instead study the possibility that the large scale temperature anisotropies are not enhanced because of a suppression of the scalar power at large scales.	contribution 1.00	0.44	0.24	hedged possibility 0.91
s6	Such a situation can be achieved for instance by a sudden change of the speed of the inflaton (by about 14 %), and we show that it fits the temperature anisotropies and polarization data considerably better than a constant running (its chi^2 improves by ~ 7.5 over that of the constant running, at the cost of one more parameter).	result 0.81	0.95	0.68	asserted 0.99
s7	We also consider the possibility that the large scale temperature fluctuations are suppressed by an anti-correlation between tensor and scalar modes.	contribution 0.97	0.53	0.05	hedged possibility 0.91
s8	Unfortunately, while such effect does affect the temperature fluctuations at large scales, it does not affect the temperature power spectrum and cannot, therefore, help in reconciling a large value of r with the limits from temperature fluctuations.	result 0.90	0.71	0.11	asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.93 · evidence from analysis of existing data 0.90.

What was examined, and what was not

sources read

arXiv listing abstract v4

not examined

full text
figures and tables
references and citing sentences
relations to other papers

levels run

P abstract

not run

S sections
T body sentences
C citations
R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

Figures

**Figure 1.** The total contribution to the T T spectrum from scalar and tensors. The black (solid) curve shows the best-fit suppression (or Starobinsky) model with r = 0.18 from the MCMC chains. The tensor contribution compensates for the loss of large-scale scalar power but also allows a better fit to the low points in the range 20 < ` < 30. The red (dashed) model is the best-fit model from the “base r” Planck+WP MCMC runs with r = 0.004. affect the temperature power spectrum, and will therefore not help reconcile the constraints on r from T T with those from BB spectra. The plan of the paper…

**Figure 2.** Primordal scalar power spectrum with the best fit parameters for (i) a constant spectral index, (ii) a constant running, and (iii) the inflation potential (2.1) with a ∆ = 0.14 change in slope. This corresponds to a ∼ 26% suppression at large scales. The ` values indicated near the x−axis correspond to the multipole that is mostly sensitive to the mode with that momentum k. 10 1 10 2 10 3 ` 10 -7 10 -6 10 -5 10 -4 10 -3 10 -2 10 -1 ` ( ` + 1 ) C` = 2 ¼ Suppr., Planck+WP+BICEP2 Planck+WP, r =0:004 BICEP2 BB data

**Figure 3.** The BB spectra for the same two models shown in

**Figure 4.** The marginalised, normalised, 1 and 2-D posteriors for k? and ∆. The parameters are well constrained by the T T data. We recall that the best fit value ∆ = 0.14 corresponds to a ∼ 26% suppression of the scalar power at large scales. Planck+WP+BICEP2 ∆Np χ 2 ∆χ 2 r ΛCDM + tensor – 9853.104 – 0.18 ΛCDM + tensor + αs +1 9846.426 -6.68 0.18 Suppression +2 9838.87 -14.23 0.18

**Figure 5.** The marginalised, normalised, 1 and 2-D posteriors for k? and βs in eq. (A.1). A Step-function suppression of the scalar power In this Appendix we consider the possibility of a step-function suppression of the scalar power: Ps (k) = Aβs k ns−1 , (A.1) with βs = 1 for k ≥ k∗ and βs < 1 for k < k∗. This parametrization should be compared for instance with the power spectrum (2.2) obtained in the Starobinsky model (2.1), with the identification βs ≡ (1 − ∆)2 . As compared to that model, this parametrization does not have the “ringing” in the power visible in

Figures reproduced from arXiv:1403.4596 by the authors.

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Forward citations

Cited by 10 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Wiggly Whipped Inflation
astro-ph.CO 2014-05 conditional novelty 5.0 of 10

Adding a smoothed step to the Whipped Inflation potential generates wiggles in the primordial power spectrum that improve fits to Planck low- and high-multipole temperature data while preserving BICEP2-scale tensors.
Blue Tensor Spectrum from Particle Production during Inflation
astro-ph.CO 2014-05 conditional novelty 5.0 of 10

Gauge quanta produced by a rolling axion during inflation can source a blue gravitational-wave spectrum, reconciling BICEP2 and Planck, and the axion potential is in principle reconstructable from that spectrum.
A No-Scale Inflationary Model to Fit Them All
hep-ph 2014-05 conditional novelty 5.0 of 10

A single no-scale supergravity model with two fields reproduces both quadratic and Starobinsky-like inflation as limits of one angle, spanning tensor-to-scalar ratios from roughly 0.09 to 0.003 at n_s about 0.96.
Neutrinoful Universe
hep-ph 2014-04 conditional novelty 5.0 of 10

The B-L Higgs inflaton, non-thermal leptogenesis, and PeV right-handed neutrino dark matter can be combined in one sector, with the PeV dark matter decay explaining the IceCube neutrino excess for a lifetime of order 10^28 s.
Neutrinos help reconcile Planck measurements with both Early and Local Universe
astro-ph.CO 2014-03 conditional novelty 5.0 of 10

Adding one massive sterile neutrino to ΛCDM reconciles Planck with BICEP2, local H0, and cluster abundances at 3.8 to 4 sigma joint significance.

Show 5 more citing papers

Cosmological constraints on neutrinos after BICEP2
astro-ph.CO 2014-04 conditional novelty 4.0 of 10

Combining Planck, BICEP2, and local astrophysical data, the authors report a ~4-sigma preference for nonzero neutrino mass and a ~0.5 eV sterile neutrino, and argue these models relieve the Planck-BICEP2 tensor-to-sca...
Natural Chaotic Inflation and UV Sensitivity
hep-th 2014-04 conditional novelty 4.0 of 10

Quadratic chaotic inflation from an axion-4-form effective theory is argued to be viable at the GUT scale, with UV corrections near M_GUT producing potentially observable changes to the scalar and tensor spectra.
Whipped inflation
astro-ph.CO 2014-04 conditional novelty 4.0 of 10

A two-stage inflaton potential with an initial fast-roll phase suppresses large-scale scalar power and raises the tensor-to-scalar ratio, improving the joint fit to Planck and BICEP2 data over a power-law spectrum.
Multi-Natural Inflation in Supergravity and BICEP2
hep-ph 2014-03 conditional novelty 4.0 of 10

A two-sine-wave inflaton potential can span a broad region of (n_s, r) space, including n_s near or above unity with r around 0.1 to 0.2, so the model is not excluded by BICEP2.
Closed String Thermodynamics and a Blue Tensor Spectrum
astro-ph.CO 2014-03 conditional novelty 3.0 of 10

String gas cosmology's Hagedorn phase predicts a blue tensor tilt with a complementary red scalar tilt and large r, a falsifiable alternative to inflation that the authors argue BICEP2 data should be tested against.

How the literature uses it

53 arXiv papers cite this in 73 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 44 sentences without a confident label

Uses its data or values 1 paper

Assuming the reported BICEP2 measurement of $r ∼0.2$ (now known to have been confused by dust), Contaldi et al. estimated that $C(k)$ could be roughly of order $0.14$ [ref] .

The hemispherical asymmetry from a scale-dependent inflationary bispectrum · The perturbed two-point function · 0.88

Compares with it 2 papers

[ref] finds that a power suppression of $≃35%$ to be the best fit to Planck+BICEP data and we find a $≃10%$ suppression due to the fast roll stage, we emphasize that our analysis was only a leading order correction and further numerical effort would be needed to fully ascertain the effect of large scale power suppression due to a fast roll scenario.

Tensor to scalar ratio and large scale power suppression from pre-slow roll initial conditions · Fast roll corrections to power spectra: · 0.95
For these parameter choices the low-$ℓ$ suppression $C(k)$ may be larger than the approximate bound $C(k) ≲0.14$ suggested by Contaldi et al. [ref] .

Implications of the CMB power asymmetry for the early universe · Building a successful model · 0.83

Cites it as support 5 papers

It has been showed in a number of recent papers [ref] that a drop in large scale scalar primordial power spectrum (PPS) allows tensor-to-scalar ratio, $r$ to be large and helps to fit the Planck and BICEP2 data simultaneously and significantly better than power law scalar PPS.

Whipped inflation · Introduction · 0.96
First order in slow roll may seem restrictive in the context of exploring structure in the inflationary trajectories but the data is suggesting a transition between two regimes that are well within the slow roll approximation [ref] and this should therefore be sufficient to define the trajectories in the observational window.

BICEP's acceleration · Sampling the acceleration · 0.99
We [ref] and others [ref] also showed that a step in the primordial perturbation scalar spectrum would also provide a good fit to the Planck TT power spectrum.

Wiggly Whipped Inflation · Step in the primordial perturbation spectrum · 0.96

Cites it as background 19 papers

To relieve this tension, some possible extensions to the $Λ$CDM+$r$ model have been discussed such as the ruining spectral index [ref] introduced by BICEP2 (see also in Refs. [ref] ), the additional relativistic degrees of freedom beyond the three active neutrinos and photons [ref] , the suppression of the adiabatic perturbations on large scales [ref] , the blue tilted tensor [ref] , and the isocurvature mode [ref] and so on.

Reconciling the Tension Between Planck and BICEP2 Through Early Dark Energy · Introduction · 0.82
Inflationary modifications include a large running of the scalar tilt [ref] ; more explicit features in the inflationary scalar spectra [ref] ; or anticorrelated isocurvature perturbations [ref] .

Neutrinos help reconcile Planck measurements with both Early and Local Universe · Introduction · 0.84
Some possible extensions of the model to resolve the tension have been discussed since the data release of BICEP2 such as the running spectral index [ref] , the suppression of the adiabatic perturbations on large scales [ref] , the presence of the extra relativistic particles [ref] , blue-tilted tensor spectrum [ref] , the existence of anti-correlated isocurvature mode [ref] , and so on.

Isocurvature perturbations and tensor mode in light of Planck and BICEP2 · Introduction · 0.89

What it cites · 33 sentences without a confident label

Uses data or values from 3 papers

The BICEP2 experiment [ref] has observed a $B$-mode polarization of the Cosmic Microwave Background (CMB) that can be well fit by a lensed-$Λ$CDM + tensor theoretical model, with tensor-to-scalar ratio $r=0.2^+0.07_-0.05$, with $r=0$ disfavored at $7σ$.

BICEP2 I: Detection Of B-mode Polarization at Degree Angular Scales · Introduction · 0.94
From Figure 5 of [ref] we infer that a value $α_s ∼- 0.02$ is required to reconcile the temperature data with $r =0.2$.

Planck 2013 results. XXII. Constraints on inflation · Introduction · 0.98
For simplicity we carry out a MCMC exploration of the reduced parameter space spanned by $τ$ the optical depth to reionization, $n_s$ the scalar spectral index, $ln(10^10 A)$ the logarithm of the primordial curvature perturbation, $r$ the tensor-to-scalar ratio, $k_⋆$, and $Δ$ and keep all other cosmological and nuisance parameters fixed to the best-fit values of the “base r” Planck+WP run reported in [ref] .

Planck 2013 results. XVI. Cosmological parameters · Suppression of large scale scalar modes · 0.95

Discussion

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