New modified cosmology from a new generalized entropy

TL;DR

This paper introduces a new generalized entropy-based approach to modified cosmology, deriving a dark energy model with diverse behaviors, including quintessence, phantom, and cosmological constant scenarios, consistent with the universe's thermal history.

Contribution

It develops a novel generalized entropy framework that leads to a modified cosmological model with a flexible dark energy component and richer dynamics than previous entropic cosmologies.

Findings

The universe's thermal history is preserved in the model.

Dark energy can be quintessence-like, phantom-like, or cross the phantom divide.

The model predicts a stable cosmological constant in the far future.

Abstract

We develop new modified cosmological scenarios by applying the first law of thermodynamics at the Universe horizon, utilizing a new entropic functional that generalizes the standard Boltzmann-Gibbs-Shannon entropy. In particular, starting from the general theory of entropy in terms of the probability distribution over the accessible microstates, and by imposing violation of the separability requirement and thus considering a generalized microstate scaling, we result to a generalized entropy expression, which applied in systems with boundaries yields a generalized holographic-like area-law scaling with two exponents. Hence, incorporating it within the gravity-thermodynamics framework, we result to a modified cosmological scenario with additional terms, which eventually give rise to an effective dark energy sector. We extract analytical expressions for the dark energy density and equation-of-state parameters, and we show that the Universe experiences the usual thermal history, with the sequence of matter and dark-energy eras. Additionally, depending on the values of the entropic exponents, the dark energy can be quintessence-like, phantom-like or experience the phantom-divide crossing during its evolution, ultimately stabilizing at the cosmological constant value in the asymptotic far future, a behavior richer than other entropic modified cosmologies.