PaperlayerView exact revision on arXiv

Source-linked AI summary

Impact of the Hubble tension on the $r$-$n_s$ contour

Jun-Qian Jiang, Gen Ye, Yun-Song Piao

arXiv:2303.12345v2astro-ph.COgr-qchep-th

TL;DR

The paper examines how an EDE resolution of the Hubble tension affects inflation constraints that have been derived under ΛCDM. Using recent CMB data and forecasts for CMB-S4 and LiteBIRD, it finds shifts in n_s and a slightly tighter upper limit on r, with future observations able to distinguish inflation models if EDE is present.

  • Problem

    Inflation constraints on n_s and r are based on ΛCDM, while a proposed EDE resolution of the Hubble tension can alter those constraints.

    Source: §1 · p. 2

  • Method

    The authors analyze EDE scenarios with current CMB datasets and forecast how CMB-S4 and LiteBIRD would constrain inflation models.

    Source: §2.1 · p. 4, §2.2 · p. 5, §3 · p. 7

  • Results

    With EDE, |n_s−1| ≲O(0.01), while r < 0.028 with Planck PR4+BK18 and r < 0.030 with Planck PR4+ACT+SPT+BK18.

    Source: §4 · p. 9

  • Takeaways & Limitations

    If EDE is present, CMB-S4 and LiteBIRD are projected to distinguish inflation models allowed by present observations.

    Source: §4 · p. 9

    The analysis forces the Hubble tension and does not address other inconsistencies such as the S8 tension.

    Source: §4 · p. 9

Abstract

from arXiv · show

The injection of early dark energy (EDE) before the recombination, a possible resolution of the Hubble tension, will not only shift the scalar spectral index $n_s$ towards $n_s=1$, but also be likely to tighten the current upper limit on tensor-to-scalar ratio $r$. In this work, with the latest CMB datasets (Planck PR4, ACT, SPT and BICEP/Keck), as well as BAO and SN, we confirm this result, and discuss its implication on inflation. We also show that if we happen to live with EDE, how the different inflation models currently allowed would be distinguished by planned CMB observations, such as CMB-S4 and LiteBIRD.

1 Introduction

The introduction frames inflation constraints on n_s and r as dependent on ΛCDM, then motivates testing how an EDE resolution of the Hubble tension changes them. It also sets out forecasts for distinguishing inflation models with upcoming CMB observations.

1 Introduction

  • Current ΛCDM-based constraints are n_s = 0.965 ± 0.004 (68% CL) and r < 0.036 (95% CL), making their model dependence central to the paper’s motivation.The introduction cites Planck combined with other datasets for n_s and Planck with BICEP/Keck for r.Source: §1 · p. 2
  • EDE before recombination lowers the sound horizon so H0 rises, but this proposed Hubble-tension resolution also changes the interpretation of inflation constraints.The authors note that EDE injection can shift n_s toward 1 and may tighten the upper limit on r.Source: §1 · p. 2
  • For H0 ≳72 km/s/Mpc, prior studies find n_s shifts to n_s = 1 with |n_s −1| ∼O(0.001), while the current limit on r may also change.The introduction presents these effects as results reported in earlier studies, not as this paper’s findings.Source: §1 · p. 2
  • Here, EDE means a pre-recombination modification to ΛCDM, with post-recombination evolution remaining ΛCDM-like.This is the paper’s stated convention for EDE.Source: §1 · p. 2
  • The study tests whether the r−n_s result remains credible using Planck PR4 and recent ACT and SPT-3G data, alongside the BICEP/Keck context.The stated analysis focuses on EDE as a possible resolution of the Hubble tension.Source: §1 · p. 3
  • CMB-S4 plus LiteBIRD are forecast to reach σ(n_s) ∼0.005 and σ(r) < 10−3, potentially distinguishing inflation models allowed by current observations if EDE is present.The forecast assumes AdS-EDE; the authors expect similar performance for other EDE models.Source: §1 · p. 3

2 Results with current data

Using current CMB, BAO, and SN combinations selected to allow tension-resolving EDE, the analysis finds a shift in the n_s-r contour and a tighter upper limit on r. It also finds power-law and ϕp inflation compatible with EDE when inflation ends during deep slow roll.

2.1 Datasets and models

  • The analysis combines Planck and BICEP/Keck, with or without ACT and SPT small-scale CMB data, and includes BAO and SN in all datasets.For ground-based small-scale CMB combinations, PR4 TT is cut to ℓ < 1000 and hillipop EE to ℓ > 150.Source: §2.1 · p. 4
  • The study tests axion-like and AdS EDE models, using zc and fEDE as phenomenological parameters and sampling Θini for axion-like EDE.The axion-like model uses an oscillation phase for fast decay, while AdS-EDE uses an AdS phase.Source: §2.1 · pp. 4–5
  • Cobaya MCMC sampling and modified CLASS calculations are used to constrain the cosmological and EDE parameters.The sampled parameters include the six standard ΛCDM parameters and the tensor-to-scalar ratio r.Source: §2.1 · p. 4
  • The authors report that their joint constraint does not depend on the BAO-data selection, including whether Lyman-α BAO is used.The text notes a possible inconsistency associated with Lyman-α BAO.Source: §2.1 · p. 4

2.2 Results

  • In the selected EDE-like models with H0 ≳ 72 km/s/Mpc, n_s shifts close to 1.The shift is described as a common result of prerecombination Hubble-tension resolutions that do not modify recombination physics.Source: §2.2 · pp. 5–6
  • r < 0.028 in AdS-EDE, compared with r < 0.0352 for ΛCDM with PR4+ACT+SPT, with enhanced lensing between 200 < ℓ < 800 contributing to the tighter EDE limit.The authors attribute the stronger lensing spectrum to slight uplifts of ωm and As in EDE models.Source: §2.2 · p. 6
  • Power-law and ϕp inflation, previously disfavored in ΛCDM, become compatible with EDE when inflation ends in deep slow roll and N* ≫ 60.The Figure 2 caption distinguishes standard and hybrid model predictions on the n_s-r contour.Source: §2.2 · p. 7, Figure 2 · p. 7

3 Forecast with CMB-S4 and LiteBIRD

Under an AdS-EDE fiducial model, the forecast compares CMB-S4 alone with CMB-S4 plus LiteBIRD at two assumed values of r. The resulting contours distinguish inflation models differently depending on whether r is undetected or detected at 0.003.

3 Forecast with CMB-S4 and LiteBIRD

  • CMB-S4 is forecast over fsky = 0.4 and 20 < ℓ < 5000, while LiteBIRD uses fsky = 0.9 and 2 < ℓ < 200; CMB-S4 sets ℓmin = 200 to avoid correlation.The noise power spectrum and delensing assumptions are given in Appendix C.Source: §3 · pp. 7–8
  • The parameter covariance forecast is obtained by inverting the Fisher matrix, defined as the expectation of the log-likelihood Hessian.The forecast uses the relevant noise and power spectra in the Fisher calculation.Source: §3 · p. 8
  • The contours use AdS-EDE best-fit parameters from PR4+BK18, with r fixed to 0 or 0.003, and compare CMB-S4 with CMB-S4+LiteBIRD.The forecast uses the fiducial cosmological values listed in Table 2; r was fixed to 0 when searching for best-fit values.Source: Figure 3 · p. 8, §3 · p. 8, Table 2 · p. 9
  • At r = 0, ϕp inflation (p > 2/3) and power-law inflation with a hybrid end are ruled out at 2σ, while Starobinski inflation with N*≈300 remains consistent.At r = 0.003, ϕp inflation (p > 2/3), power-law inflation, and Starobinski inflation are ruled out at 2σ; only hybrid ϕp inflation with p < 2/3 might survive.Source: §3 · pp. 8–9, Figure 3 · p. 8

4 Conclusion

With the latest CMB datasets, the analysis finds EDE-compatible constraints with n_s close to 1 and slightly tighter upper limits on r. It also concludes that inflation-model viability depends on the EDE scenario and that other cosmological tensions may affect the contours.

4 Conclusion

  • For EDE, |n_s−1| ≲ O(0.01), with r < 0.028 for Planck PR4+BK18 and r < 0.030 for Planck PR4+ACT+SPT+BK18.The upper limits are described as slightly tighter and consistent with the Planck PR3+BK18 result [21].Source: §4 · p. 9
  • Inflation models ruled out under ΛCDM, including ϕp inflation and Starobinski inflation, can become possible in corresponding EDE models with hybrid variants.The paper links this possibility to inflation ending through a waterfall instability while the inflaton remains in a deep slow-roll region.Source: §4 · p. 9
  • CMB-S4 plus LiteBIRD is forecast to reach σ(n_s) ∼ 0.005 and σ(r) < 10^-3, distinguishing inflation models allowed by current observations if EDE is realized.Source: §4 · p. 9
  • The analysis forces only the Hubble tension; other inconsistencies, including the S8 tension, may also affect the r−n_s contour and inflation-model implications.Source: §4 · pp. 9–10

A Priors for cosmological parameters

The listed priors are flat, with specified parameters applying only to EDE models, the axion-like EDE model, or Appendix B.

A Priors for cosmological parameters

  • All listed parameter priors are flat; log10(1 + zc) and fEDE apply only to EDE models, Θi only to axion-like EDE, and n_s and α_s only to Appendix B.Source: Table 3 · p. 10

B Results for nt and αs

The EDE models yield lower r2 upper limits than ΛCDM, with the difference more pronounced than for r_pivot. EDE has no significant reported effect on n_t or α_s; α_s differences mainly reflect CMB dataset combinations.

B Results for nt and αs

  • Figure 4 shows marginalized posteriors for n_t and α_s; EDE has no significant effect on either, while α_s differences mainly reflect CMB dataset combinations.Source: B Results for nt and αs · p. 10, Figure 4 · p. 11
  • With PR4+ACT+SPT, r2 < 0.0457 for AdSEDE and r2 < 0.0566 for axion-like EDE; with PR4, AdSEDE has r2 < 0.0424 (95% CL).All three EDE bounds are reported at 95% CL.Source: B Results for nt and αs · pp. 10–11
  • EDE r2 upper limits are lower than ΛCDM limits, with a more significant discrepancy than for r_pivot, attributed mainly to larger EDE lensing near ℓ∼250.For PR4, ΛCDM has r2 < 0.0653; for PR4+ACT+SPT, it has r2 < 0.0656 (both 95% CL).Source: B Results for nt and αs · p. 11

C On noise power spectrum and delensing

The forecast setup specifies noise assumptions for CMB-S4 and LiteBIRD, models delensing and foregrounds, and presents marginalized parameter posteriors across models and datasets.

C On noise power spectrum and delensing

D Marginalized posterior distributions for all cosmological parameters

Figure 6 shows marginalized cosmological-parameter posteriors across models and datasets, while Table 4 reports ΛCDM parameter intervals for different datasets.

D Marginalized posterior distributions for all cosmological parameters

  • Figure 6 presents marginalized posteriors for all cosmological parameters across models and datasets, with the R21 constraint on H0 marked as a gray band.Source: Figure 6 · p. 13
  • Table 4 reports 68% confidence intervals for ΛCDM parameters across datasets, with best-fit values in parentheses and one-tailed 95% intervals.Source: Table 4 · p. 13
  • BK18 is included in every dataset shown in Table 4.Source: Table 4 · p. 13
Loading 2303.12345v2…