Raychaudhuri equation and Bouncing cosmology

TL;DR

This paper explores bouncing cosmology within FLRW spacetime, analyzing the geometry at bounce points, using Raychaudhuri equation to classify singularities, and discussing oscillatory models via geodesic behavior and harmonic oscillator analogy.

Contribution

It provides a comprehensive analysis of bouncing points using Raychaudhuri equation and introduces an oscillatory bouncing model based on harmonic oscillator analogy.

Findings

Classification of bounce points as regular or singular using Raychaudhuri equation.

Analysis of geodesic congruence behavior near bounce points.

Proposal of an oscillatory bouncing model through harmonic oscillator analogy.

Abstract

The present work deals with an exhaustive study of bouncing cosmology in the background of homogeneous and isotropic Friedmann-Lemaitre-Robertson-Walker space-time. The geometry of the bouncing point has been studied extensively and used as a tool to classify the models from the point of view of cosmology. Raychaudhuri equation (RE) has been furnished in these models to classify the bouncing point as regular point or singular point. Behavior of time-like geodesic congruence in the neighbourhood of the bouncing point has been discussed using the Focusing Theorem which follows as a consequence of the RE. An analogy of the RE with the evolution equation for a linear harmonic oscillator has been made and an oscillatory bouncing model has been discussed in this context.