Observational constraints on Tsallis modified gravity

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 similar to 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-Lemattre-Robertson-Walker 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, weak lensing, supernovae, baryon acoustic oscillations, and redshift-space distortions 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.

Automated summary

The thermodynamics-gravity conjecture suggests a reciprocal relationship between the gravitational field equations and the first law of thermodynamics. By incorporating non-extensive Tsallis entropy and applying the Clausius relation, gravitational field equations were derived, and a cosmological model based on Tsallis modified gravity was constructed. Observational data was used to constrain the cosmological parameters of the model, which showed that the model may alleviate tensions in the structure growth parameter sigma(8).