Cosmological Hints of Modified Gravity ?

TL;DR

This work tests deviations from General Relativity in cosmic structure growth using Planck 2015 data within a phenomenological MG framework that introduces μ(a) and η(a) and a derived lensing potential Σ. The authors analyze Planck TT, Planck pol, Planck lensing, and weak lensing data with MGCAMB and CosmoMC, exploring MG parameters E11 and E22 alongside the standard ΛCDM parameters and several extensions. They find MG hints at about 95% c.l. with Planck TT, strengthened by WL but weakened by CMB lensing, with τ ≈ 0.059 and σ8 ≈ 0.816, and a potential reconciliation of the A_lens anomaly; however, including lensing data reduces the significance, highlighting sensitivity to data choices and degeneracies with N_eff and Y_P. Overall, MG remains a plausible but tentative explanation for current tensions, calling for further data to confirm or refute its role in cosmology.

Abstract

The recent measurements of Cosmic Microwave Background temperature and polarization anisotropies made by the Planck satellite have provided impressive confirmation of the $Λ$CDM cosmological model. However interesting hints of slight deviations from $Λ$CDM have been found, including a $95 \%$ c.l. preference for a "modified gravity" structure formation scenario. In this paper we confirm the preference for a modified gravity scenario from Planck 2015 data, find that modified gravity solves the so-called $A_{lens}$ anomaly in the CMB angular spectrum, and constrains the amplitude of matter density fluctuations to $σ_8=0.815_{-0.048}^{+0.032}$, in better agreement with weak lensing constraints. Moreover, we find a lower value for the reionization optical depth of $τ=0.059\pm0.020$ (to be compared with the value of $τ= 0.079 \pm 0.017$ obtained in the standard scenario), more consistent with recent optical and UV data. We check the stability of this result by considering possible degeneracies with other parameters, including the neutrino effective number, the running of the spectral index and the amount of primordial helium. The indication for modified gravity is still present at about $95\%$ c.l., and could become more significant if lower values of $τ$ were to be further confirmed by future cosmological and astrophysical data.

Figures (4)

• Figure 1: Constraints at $68 \%$ and $95 \%$ confidence levels on the $\Sigma_0-1$ vs $\tau$ plane (top panel) and on the $\Sigma_0-1$ vs $H_0$ plane (bottom panel) from the Planck TT and Planck pol datasets. The $6$ parameters of the $\Lambda$CDM model are varied. Notice that $\Sigma_0$ is different from one (dashed vertical line) at about $95$ % confidence level. A small degeneracy is present between $\Sigma_0$ and $\tau$: smaller optical depths are more compatible with the data if $\Sigma_0$ is larger than one (see top panel). Another degeneracy is present with the Hubble constant: larger values of the Hubble constant are more compatible with the considered data in case of $\Sigma_0$ different from one (bottom panel).
• Figure 2: Constraints at $68 \%$ and $95 \%$ confidence levels on the $\Sigma_0-1$ vs $A_{\rm lens}$ plane from the Planck TT and Planck pol datasets. A strong degeneracy is present between $\Sigma_0$ and $A_{\rm lens}$: larger values of $A_{\rm lens}$ are more compatible with the data if $\Sigma_0$ is smaller than one.
• Figure 3: Constraints at $68 \%$ and $95 \%$ confidence levels on the $\Sigma_0-1$ vs $N_{\textrm{eff}}$ plane from the Planck TT and Planck polarization datasets. Notice that $\Sigma_0$ is different from unity (dashed vertical line) at about the $95$ % confidence level. A small direction of degeneracy is present between $\Sigma_0$ and $N_{\textrm{eff}}$: larger $N_{\textrm{eff}}$ are more compatible with the data if $\Sigma_0$ is larger than one in case of the Planck TT dataset.
• Figure 4: Constraints at $68 \%$ and $95 \%$ confidence levels on the $\Sigma_0-1$ vs $dn_s/dlnk$ plane (top panel) and on the $\Sigma_0-1$ vs $Y_p$ plane (bottom panel) from the Planck TT and Planck pol datasets. Notice that $\Sigma_0$ is different from unity (dashed vertical line) at about $95$ % confidence level. There is virtually no degeneracy between $\Sigma_0$, the running of the scalar spectral index $dn_s/dlnk$ and the primordial helium abundance.