Precision Cosmology and Hubble tension in the era of LSS surveys

TL;DR

This paper develops a relativistic framework to assess how cosmic inhomogeneities affect Hubble constant measurements, showing future deep surveys can achieve sub-0.1% precision despite stochastic uncertainties.

Contribution

It introduces a relativistic approach linking luminosity distance fluctuations to parameter estimation uncertainty, improving understanding of cosmic variance in Hubble constant measurements.

Findings

Cosmic variance in H0 measurement will be below 0.1%.

Deep surveys will yield more precise H0 estimates than local methods.

Intrinsic uncertainties from inhomogeneities are minimal for future surveys.

Abstract

We present a fully relativistic framework to evaluate the impact of stochastic inhomogeneities on the prediction of the Hubble-Lema\^itre diagram. In this regard, we relate the fluctuations of the luminosity distance-redshift relation in the Cosmic Concordance model to the intrinsic uncertainty associated to the estimation of cosmological parameters from high-redshift surveys (up to z = 4). Within this framework and according to the specific of forthcoming surveys as Euclid Deep Survey and LSST, we show that the cosmic variance associated with the measurement of the Hubble constant will not exceed 0.1 $\%$. Thanks to our results, we infer that deep surveys will provide an estimation of the the Hubble constant $H_0$ which will be more precise than the one obtained from local sources, at least in regard of the intrinsic uncertainty related to a stochastic distribution of inhomogeneities.