Parameter discordance in Planck CMB and low-redshift measurements: projection in the primordial power spectrum

TL;DR

This paper investigates how discrepancies between Planck CMB data and low-redshift measurements affect the inferred shape of the primordial power spectrum, using a non-parametric reconstruction method without extending the standard cosmological model.

Contribution

It introduces a modified Richardson-Lucy algorithm to reconstruct the primordial power spectrum consistent with both Planck and local measurements, addressing parameter discordance.

Findings

Reconstructed PPS aligns with Planck data and local H0 measurements.

Improves consistency of S8 and sigma8 with weak lensing surveys.

Demonstrates the impact of parameter discordance on primordial spectrum shape.

Abstract

We discuss the discordance between the estimated values of the cosmological parameters from Planck assuming the concordance $\Lambda$CDM model and low-redshift measurements. In particular, we consider the Hubble constant mismatch between Planck temperature constraint for the $\Lambda$CDM model and the Riess et. al. local measurements as well as the discordance between the estimated value of $S_8$ from Planck and some weak lensing surveys such as Kilo Degree Survey (KiDS-450) and Dark Energy Survey (DES) observations. The discordance can come from a wide range of non-standard cosmological or astrophysical processes as well as from some particular systematics of the observations. In this paper, without considering any particular astrophysical process or extension to the standard model at the background level, we seek solely to project the effect of these differences in the values of the key cosmological parameters on to the shape of the primordial power spectrum (PPS). In order to realise this goal, we uncover the shape of the PPS by implementing the Modified Richardson-Lucy algorithm (MRL) that fits the Planck temperature data as acceptably as the case of the standard model of cosmology, but with a Hubble constant consistent with local measurements as well as improving the consistency between the derived $S_8$ and $\sigma_8$ parameters with estimations of the weak lensing surveys.