Cosmological dynamics with modified induced gravity on the normal DGP branch

TL;DR

This paper explores the cosmological behavior of a modified gravity model inspired by DGP scenarios, analyzing stability and late-time acceleration solutions using phase space methods.

Contribution

It introduces a phase space analysis of a modified induced gravity on the normal DGP branch, identifying stable de Sitter attractors linked to late-time cosmic acceleration.

Findings

Existence of a stable de Sitter point in the phase space.

Stability of the de Sitter attractor depends on the form of the $f(R)$ function.

The model can account for late-time cosmic speed-up.

Abstract

In this paper we investigate cosmological dynamics on the normal branch of a DGP-inspired scenario within a phase space approach where induced gravity is modified in the spirit of $f(R)$-theories. We apply the dynamical system analysis to achieve the stable solutions of the scenario in the normal DGP branch. Firstly, we consider a general form of the modified induced gravity and we show that there is a standard de Sitter point in phase space of the model. Then we prove that this point is stable attractor only for those $f(R)$ functions that account for late-time cosmic speed-up.