On the cosmological viability of the Hu-Sawicki type modified induced gravity

TL;DR

This paper examines the cosmological viability of a Hu-Sawicki type modified induced gravity model within the DGP braneworld framework, analyzing its stability, phase space, and expansion history to assess its potential as a realistic cosmological model.

Contribution

It provides a dynamical system analysis of the $f(R)$-DGP model, identifying stable de Sitter solutions and exploring their stability conditions and cosmological implications.

Findings

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

The stability of the de Sitter point depends on the effective equation of state.

The model exhibits an effective phantom-like behavior in its evolution.

Abstract

It has been shown recently that the normal branch of a DGP braneworld scenario self-accelerates if the induced gravity on the brane is modified in the spirit of $f(R)$ modified gravity. Within this viewpoint, we investigate cosmological viability of the Hu-Sawicki type modified induced gravity. Firstly, we present a dynamical system analysis of a general $f(R)$-DGP model. We show that in the phase space of the model, there exist three standard critical points; one of which is a de Sitter point corresponding to accelerating phase of the universe expansion. The stability of this point depends on the effective equation of state parameter of the curvature fluid. If we consider the curvature fluid to be a canonical scalar field in the equivalent scalar-tensor theory, the mentioned de Sitter phase is unstable, otherwise it is an attractor, stable phase. We show that the effective equation of state parameter of the model realizes an effective phantom-like behavior. A cosmographic analysis shows that this model, which admits a stable de Sitter phase in its expansion history, is a cosmologically viable scenario.