Cosmological dynamics and structure formation in Tsallis-Cirto entropy-inspired modified gravity

Abstract

We explore the cosmological dynamics and formation of structures within the Tsallis-Cirto modified gravity framework with a model parameter $β$ that is inspired by nonextensive statistics. By applying the gravity-thermodynamics conjecture, we modify the Friedmann equations and the evolution of the Hubble parameter. The impact of the Tsallis-Cirto entropy on different cosmographic parameters and the development of the linear matter overdensities have been analyzed by formulating perturbed field equations using the spherical collapse approach in a flat Friedmann-Lemaître-Robertson-Walker background. We present a novel and established diagnostic approach to distinguish among distinct cosmological models compared to flat and non-flat $Λ$CDM scenarios, discovering that the Tsallis-Cirto entropy-inspired modified cosmology ($β\ne 1$) successfully withstands all tests, contradicting both the flat and non-flat $Λ$CDM models. This model also meets the conditions for the Universe to reach thermodynamic equilibrium in the far future. Additionally, we investigate the halo mass function and cluster number counts within this modified gravity framework. All findings are compared to the fiducial $Λ$CDM profile, indicating that the added entropic correction affects the history of expansion, the growth rate of structures, and the dark matter halo abundance. We find that the more massive structures are less abundant and develop at later times, which aligns with the hierarchical model of formation of large-scale structures.