Universe With Time Dependent Deceleration Parameter and $\Lambda$ Term in General Relativity

TL;DR

This paper derives new exact solutions to Einstein's field equations for an LRS Bianchi type-I universe with a time-dependent deceleration parameter, exploring exponential, polynomial, and sinusoidal models in light of recent supernova observations.

Contribution

It introduces a novel class of solutions with a time-dependent deceleration parameter, expanding the understanding of universe models in general relativity.

Findings

Three universe models: exponential, polynomial, sinusoidal.

Models align with recent supernovae Ia observations.

Provides exact solutions for Einstein's field equations.

Abstract

A new class of exact solutions of Einstein's field equations with perfect fluid for an LRS Bianchi type-I spacetime is obtained by using a time dependent deceleration parameter. We have obtained a general solution of the field equations from which three models of the universe are derived: exponential, polynomial and sinusoidal form respectively. The behaviour of these models of the universe are also discussed in the frame of reference of recent supernovae Ia observations.