Cosmographic view on the $H_0$ and $\sigma_8$ tensions

TL;DR

This paper uses a model-independent cosmographic approach to analyze the tensions in $H_0$ and $\sigma_8$ measurements, finding reduced tensions compared to standard cosmological models and highlighting deviations in the jerk parameter.

Contribution

It introduces a cosmographic, model-independent framework to constrain $H_0$ and $\sigma_8$, providing new insights into existing tensions and deviations from $\Lambda$CDM predictions.

Findings

$H_0$ tension is at 2$\sigma$ with local measurements.

$\sigma_8$ tension is at 2.6$\sigma$ with Planck-CMB.

Jerk parameter deviates more than 3$\sigma$ from $\Lambda$CDM.

Abstract

Measurements of the $H_0$ and $\sigma_8$ parameters within the standard cosmological model recently highlighted significant statistical tensions between the cosmic microwave background and low-redshift probes, such as local distance ladder, weak lensing and galaxy clustering surveys. In this work, we frame geometrical distances in a model-independent way by means of cosmographic approximations in the range $z \in (0, 2.3)$ to take into account a robust dataset composed of Baryon Acoustic Oscillations (BAO), type Ia Supernovae (SN), Cosmic Chronometer (CC) data, and measurements from Redshift Space Distortions (RSD). From the joint analysis BAO\,+\,SN\,+\,CC\,+\,RSD, we find an accuracy of $\sim$1.4\% and $\sim$3.7\% on $H_0$ and $\sigma_8$, respectively. Our result for $H_0$ is at 2$\sigma$ tension with local measurements by the SH0ES team, while our $\sigma_8$ estimate is at 2.6$\sigma$ tension with Planck-CMB analysis. This inference shows a tension statistically smaller when compared to those estimated via the $\Lambda$CDM model. We also find that the jerk parameter can deviate more than 3$\sigma$ from the $\Lambda$CDM prediction. Under the same cosmographic setup, we also present results by considering a SH0ES Gaussian prior on $H_0$ that allows for improved accuracy of the parameter space of the models. The present work brings observational constraints on $H_0$ and $\sigma_8$ into a new model-independent perspective, which differs from the predictions obtained within the $\Lambda$CDM paradigm.