A flat FRW model with dynamical $\Lambda$ as function of matter and geometry

TL;DR

This paper investigates a flat FRW cosmological model with a dynamically varying cosmological constant dependent on matter and geometry, analyzing its evolution, observational constraints, and singularities within modified gravity theories.

Contribution

It introduces a new decay law for the dynamic $\Lambda$-term in flat FRW models, incorporating various existing decay laws and providing observational constraints on model parameters.

Findings

Derived constraints on cosmological parameters like $\Omega_{m_0}$ and $\Omega_{\Lambda_0}$

Analyzed the behavior of cosmological parameters in the generalized model

Discussed conditions for finite time singularities

Abstract

We revisit the evolution of the scale factor in a flat FRW spacetime with a new generalized decay rule for the dynamic $\Lambda$-term under modified theories of gravity. It analyses certain cosmological parameters and examines their behaviours in this generalized setting which includes several decay laws in the literature. We have also obtained observational constraints on various model parameters and estimated the present values of cosmological parameters $\{\Omega_{m_0}$, $\Omega_{\Lambda_0}$, $q_{0}, t_{0}$, $\omega_{0}\}$ and have discussed with various observational results. Finite time past and future singularities in this model are also discussed. \end{abstract}