Expanding, shearing and accelerating isotropic plane symmetric universe with conformal Kasner geometry

TL;DR

This paper develops a novel inhomogeneous, shearing, and accelerating universe model based on conformal Kasner geometry, demonstrating smooth, singularity-free density and pressure profiles with causal sound speeds.

Contribution

It introduces a new cosmological model using conformal transformations of Kasner spacetime, expanding the understanding of anisotropic, inhomogeneous universe dynamics.

Findings

Universe expands for negative time and collapses for positive time.

Density and pressure are smooth and free of singularities.

Fluid obeys causality with computed sound-speed index.

Abstract

We construct a model of a universe filled with a perfect fluid with isotropic particle pressure. The anisotropic plane symmetric Kasner spacetime is used as a seed metric and through a conformal mapping a perfect fluid is generated. The model is inhomogeneous, irrotational, shearing and accelerating. For negative time, the universe is expanding while for positive time it is collapsing. With the aid of graphical three dimensional plots it is established that the density and pressure hypersurfaces are smooth and singularity free. Additionally the sound-speed index is computed and the fluid obeys causality criterion.