Time variable $\Lambda$ and the accelerating Universe

TL;DR

This paper investigates a variable cosmological constant proportional to the square of the Hubble parameter, analyzing its implications for dark energy, dark matter, and the Universe's acceleration within Einstein's equations.

Contribution

It introduces a phenomenological model with a time-dependent $ ext{Lambda}$ and explores its effects on key cosmological parameters and Universe's evolution.

Findings

Deceleration parameter and equation of state are linearly related in flat Universe.

For $ ext{Alpha} = 1$, deceleration parameter equals the equation of state parameter.

Variable $ ext{Lambda}$ impacts dark energy and Universe's age considerations.

Abstract

We perform a deductive study of accelerating Universe and focus on the importance of variable time-dependent $\Lambda$ in the Einstein's field equations under the phenomenological assumption, $\Lambda =\alpha H^2$ for the full physical range of $\alpha$. The relevance of variable $\Lambda$ with regard to various key issues like dark matter, dark energy, geometry of the field, age of the Universe, deceleration parameter and barotropic equation of state has been trivially addressed. The deceleration parameter and the barotropic equation of state parameter obey a straight line relationship for a flat Universe described by Friedmann and Raychaudhuri equations. Both the parameters are found identical for $\alpha = 1$.