Cosmological Singularity and Power-Law Solutions in Modified Gravity

TL;DR

This paper investigates whether modified gravity theories can resolve the big-bang singularity through power-law solutions, finding that some theories like $f(R)$ and Brans-Dicke can, while others like Stelle gravity cannot.

Contribution

It analyzes the conditions under which various modified gravity theories can produce non-singular bouncing cosmologies with power-law solutions.

Findings

Stelle gravity does not resolve singularities.

$f(R)$ gravity and Brans-Dicke theory can resolve singularities.

Accelerating solutions are slightly favored over ekpyrotic scenarios.

Abstract

A bouncing Universe avoids the big-bang singularity. Using the time-like and null Raychaudhhuri equations, we explore whether the bounce near the big-bang, within a broad spectrum of modified theories of gravity, allows for cosmologically relevant power-law solutions under reasonable physical conditions. Our study shows that certain modified theories of gravity, such as Stelle gravity, do not demonstrate singularity resolution under any reasonable conditions, while others including $f(R)$ gravity and Brans-Dicke theory can demonstrate singularity resolution under suitable conditions. For these theories, we show that the accelerating solution is slightly favoured over ekypyrosis.