Observational constraints on Tsallis modified gravity

TL;DR

This paper derives gravitational and cosmological equations using Tsallis non-extensive entropy and constrains the model with observational data, showing it may alleviate the $\sigma_8$ tension in cosmology.

Contribution

It introduces a novel approach to modified gravity based on Tsallis entropy and derives corresponding field and Friedmann equations.

Findings

TMG model predicts lower $\sigma_8$ than $\Lambda$CDM.

TMG model better fits low redshift large scale structure data.

The model slightly alleviates the $\sigma_8$ tension.

Abstract

The thermodynamics-gravity conjecture reveals that one can derive the gravitational field equations by using the first law of thermodynamics and vice versa. Considering the entropy associated with the horizon in the form of non-extensive Tsallis entropy, $S\sim A^{\beta}$ here we first derive the corresponding gravitational field equations by applying the Clausius relation $\delta Q=T \delta S$ to the horizon. We then construct the Friedmann equations of Friedmann-Lema\^itre-Robertson-Walker (FLRW) universe based on Tsallis modified gravity (TMG). Moreover, in order to constrain the cosmological parameters of TMG model, we use observational data, including Planck cosmic microwave background (CMB), weak lensing, supernovae, baryon acoustic oscillations (BAO), and redshift-space distortions (RSD) data. Numerical results indicate that TMG model with a quintessential dark energy is more compatible with the low redshift measurements of large scale structures by predicting a lower value for the structure growth parameter $\sigma_8$ with respect to $\Lambda$CDM model. This implies that TMG model would slightly alleviate the $\sigma_8$ tension.