Big-Bounce with Finite-time Singularity: The $F(R)$ Gravity Description

Abstract

An alternative to the Big Bang cosmologies is obtained by the Big Bounce cosmologies. In this paper, we study a bounce cosmology with a Type IV singularity occurring at the bouncing point, in the context of $F(R)$ modified gravity. We investigate the evolution of the Hubble radius and we examine the issue of primordial cosmological perturbations in detail. As we demonstrate, for the singular bounce, the primordial perturbations originating from the cosmological era near the bounce, do not produce a scale invariant spectrum and also the short wavelength modes, after these exit the horizon, do not freeze, but grow linearly with time. After presenting the cosmological perturbations study, we discuss the viability of the singular bounce model, and our results indicate that the singular bounce must be combined with another cosmological scenario, or should be modified appropriately, in order that it leads to a viable cosmology. The study of the slow-roll parameters leads to the same result, indicating the singular bounce theory is unstable at the singularity point, for certain values of the parameters. We also conformally transform the Jordan frame singular bounce, and as we demonstrate, the Einstein frame metric leads to a Big Rip singularity. Therefore, the Type IV singularity in the Jordan frame, becomes a Big Rip singularity in the Einstein frame. Finally, we briefly study a generalized singular cosmological model, which contains two Type IV singularities, with quite appealing features.

IJMPD accepted

Cited by in corpus (14)

• Inflationary $\alpha$-attractors from $F(R)$ Gravity
• Deceleration versus Acceleration Universe in Different Frames of $F(R)$ Gravity
• Extended matter bounce scenario in ghost free $f(R,\mathcal{G})$ gravity compatible with GW170817
• Transformations between Jordan and Einstein frames: Bounces, antigravity, and crossing singularities
• Non-singular Bounce Cosmology from Lagrange Multiplier $F(R)$ Gravity
• Inflationary magnetogenesis with reheating phase from higher curvature coupling
• Singular $F(R)$ Cosmology Unifying Early and Late-time Acceleration with Matter and Radiation Domination Era
• Gauss-Bonnet Cosmology Unifying Late and Early-time Acceleration Eras with Intermediate Eras
• On the Viability of the Intermediate Inflation Scenario with $F(T)$ Gravity
• Effective Theory of Inflationary Magnetogenesis and Constraints on Reheating
• On the Expanding Phase of a Singular Bounce and Intermediate Inflation: The Modified Gravity Description
• Thermal Fluctuations of Dark Matter in Bouncing Cosmology
• A class of simple bouncing and late-time accelerating cosmologies in f(R) gravity
• Cosmological Study of Autonomous Dynamical Systems in Modified Tele-Parallel Gravity