Correspondence between Myrzakulov $F(R,Q)$ gravity and Tsallis cosmology

TL;DR

This paper explores the equivalence of Myrzakulov $F(R,Q)$ gravity and Tsallis cosmology at the background level, highlighting differences in perturbation behavior that could help distinguish between these models observationally.

Contribution

It establishes a correspondence between modified gravity and modified cosmology frameworks, showing they can produce identical background evolution but differ in perturbative predictions.

Findings

Both models replicate the standard cosmological sequence.

Perturbation growth and effective Newton constant differ between models.

Perturbative observables can distinguish the two frameworks.

Abstract

We investigate the correspondence between Myrzakulov $F(R,Q)$ gravity and Tsallis cosmology. The former is a modified gravity that uses both curvature and nonmetricity, while the latter is a modified cosmology arising from the gravity-thermodynamics conjecture, employing Tsallis entropy instead of the Bekenstein-Hawking one. By appropriately identifying the functional dependencies and the model parameters, we demonstrate that both frameworks can give identical background evolution, reproducing the standard cosmological sequence of matter and dark energy domination. However, their perturbation behavior exhibits differences, since the growth of density fluctuations and the effective Newton constant deviate between the two scenarios, indicating that perturbative observables, such as structure formation and weak-lensing ones, could serve as distinguishing factors between them.