A study of Raychaudhuri equation and geodesic focusing in Fractal Universe

TL;DR

This paper investigates how the Raychaudhuri equation behaves in a fractal universe, analyzing geodesic focusing and the potential to avoid the initial big-bang singularity through fractal modifications.

Contribution

It introduces a modified Raychaudhuri equation in a fractal universe and explores geodesic focusing and singularity avoidance in this novel framework.

Findings

Focusing of time-like geodesics depends on the fractal function chosen.

The sign of the convergence scalar influences the possibility of avoiding the big-bang singularity.

Certain fractal models may prevent the formation of initial singularities.

Abstract

The paper deals with the modified Raychaudhuri equation (RE) within the framework of homogeneous and isotropic Fractal Universe. Focusing of a congruence of time-like geodesics has been examined for three generic choices of the fractal function. Finally, comments on the existence and possible avoidance of the initial big-bang singularity have been made by examining the sign of convergence scalar in the fractal models under consideration.