Initial and final de Sitter universes from modified $f(R)$ gravity

TL;DR

This paper explores modified $f(R)$ gravity models that admit multiple de Sitter solutions, potentially unifying early inflation and late-time acceleration, and analyzes their stability, evolution, and thermodynamics.

Contribution

It demonstrates the existence of multiple de Sitter solutions in $f(R)$ models and explores their stability, evolution, and thermodynamic properties, proposing a unified cosmological scenario.

Findings

Multiple de Sitter solutions can be found in certain $f(R)$ models.

Some solutions are stable and others are unstable.

Models can unify early inflation with late-time acceleration.

Abstract

Viable models of modified gravity which satisfy both local as well as cosmological tests are investigated. It is demonstrated that some versions of such highly non-linear models exhibit multiply de Sitter universe solutions, which often appear in pairs, being one of them stable and the other unstable. It is explicitly shown that, for some values of the parameters, it is possible to find several de Sitter spaces (as a rule, numerically); one of them may serve for the inflationary stage, while the other can be used for the description of the dark energy epoch. The numerical evolution of the effective equation of state parameter is also presented, showing that these models can be considered as natural candidates for the unification of early-time inflation with late-time acceleration through dS critical points. Moreover, based on the de Sitter solutions, multiply SdS universes are constructed which might also appear at the (pre-)inflationary stage. Their thermodynamics are studied and free energies are compared.