A comment on power-law inflation with a dark radiation component

TL;DR

This work tests whether power-law inflation (PLI) with a free dark radiation component can reconcile the local $H_0$ measurements with Planck CMB constraints. By performing a Bayesian analysis of an extended $\Lambda$CDM model including $r$ and $N_{ m eff}$ and a PLI consistency relation $r=\frac{16 n_{\rm T} n_{\rm T}}{n_{\rm T} n_{\rm T}-2}$ with $n_{\rm T}^2 = n_{\rm S}^2-1$, the study uses Planck 2015 data plus BKP and the Planck HFI $\tau$055 prior to derive constraints. The results show that while PLI can push $N_{ m eff}$ and $H_0$ higher for some datasets, the Planck HFI $\tau$055 constraint pulls $N_{ m eff}$ back toward the standard value and reintroduces the $H_0$ tension; a nonzero $r$ is indicated in certain combinations, but the overall fit worsens, and $\sigma_8$ is driven upward, worsening weak-lensing tensions. Consequently, with the latest data, the PLI+dark radiation scenario does not provide a robust resolution to cosmological tensions and loses appeal as a solution.

Abstract

Tram et al. 2016 recently pointed out that power-law inflation in presence of a dark radiation component may relieve the 3.3 sigma tension which exists within standard LCDM between the determination of the local value of the Hubble constant by Riess et al. (2016) and the value derived from CMB anisotropy data by the Planck collaboration. In this comment, we simply point out that this interesting proposal does not help in solving the $σ_8$ tension between the Planck data and, e.g., the weak lensing measurements. Moreover, when the latest constraints on the reionization optical depth obtained from Planck HFI data are included in the analysis, the $H_0$ tension reappears and this scenario looses appeal.

Figures (4)

• Figure 1: Scattered 3D plot in the $n{_{\rm S}}$n__ S$$ versus $N_{\rm eff}$ plane, coloured by $H_0$, under the assumption of PLI.
• Figure 2: Constraints at $68 \%$ and $95 \%$ confidence levels on the $r$ vs $N_{\rm eff}$ plane under the assumption of PLI.
• Figure 3: Constraints at $68 \%$ and $95 \%$ confidence levels on the $H_0$ vs $\sigma_8$ plane under the assumption of PLI.
• Figure 4: Constraints at $68 \%$ and $95 \%$ confidence levels on the $r$ vs $n_s$ plane, without considering the PLI.