$\Lambda$-CDM Universe: A Phenomenological Approach With Many Possibilities

TL;DR

This paper proposes a phenomenological model where the cosmological constant varies with time as , deriving a dynamic equation of state and matching observational data on the universe's age and acceleration.

Contribution

It introduces a novel time-dependent  model for , providing insights into the sign flip of the deceleration parameter and aligning with observational universe age.

Findings

Derived a time-dependent equation of state parameter 

Achieved a sign flip in the deceleration parameter q

Estimated universe age consistent with observations

Abstract

A time-dependent phenomenological model of $\Lambda$, viz. $\dot \Lambda\sim H^3$ is selected to investigate the $\Lambda$-CDM cosmology. Time-dependent form of the equation of state parameter $\omega$ is derived and it has been possible to obtain the sought for flip of sign of the deceleration parameter q. Present age of the Universe, calculated for some specific values of the parameters agrees very well with the observational data.