FRW Universe with Variable $G$ and $\Lambda$-Terms

TL;DR

This paper derives new exact solutions to Einstein's equations for an FRW universe with variable G and Lambda, analyzing their behavior under different models and comparing with supernova observations.

Contribution

It introduces a new class of solutions with variable G and Lambda for FRW cosmology using variable deceleration parameter models.

Findings

Models exhibit different behaviors for G(t), Lambda(t), and density rho(t)

Solutions include exponential, polynomial, and sinusoidal forms

Models align with recent supernovae Ia observations

Abstract

A new class of exact solutions of Einstein's field equations with a perfect fluid source, variable gravitational coupling $G$ and cosmological term $\Lambda$ for FRW spacetime is obtained by considering variable deceleration parameter models for the universe. The nature of the variables $G(t)$, $\Lambda(t)$ and the energy density $\rho(t)$ have been examined for three cases : (i) exponential (ii) polynomial and (iii) sinusoidal form. The special types of models for dust, Zel'dovich and radiating universe are also mentioned in all these cases. The behaviour of these models of the universe are also discussed in the light of recent supernovae Ia observations.