# FRW dark energy cosmological model with hybrid expansion law

## TL;DR

This paper proposes a new FRW cosmological model with a hybrid expansion law that transitions from deceleration to acceleration, fitting observational supernova data and analyzing the evolution of dark energy and cosmic parameters.

## Contribution

Introduces a novel hybrid expansion law for FRW cosmology with variable dark energy equations of state, aligning with observational data.

## Key findings

- Model fits supernova data well.
- Identifies the epoch of cosmic acceleration onset.
- Describes evolution of dark energy and expansion parameters.

## Abstract

In this work, we study a cosmological model of spatially homogeneous and isotropic accelerating universe which exhibits a transition from deceleration to acceleration. For this, Friedmann Robertson Walker(FRW) metric is taken and Hybrid expansion law $a(t)=t^{\alpha} \exp(\beta t )$ is proposed and derived. We consider the universe to be filled with two types of fluids barotropic and dark energy which have variable equations of state. The evolution of dark energy, Hubble, and deceleration parameters etc., have been described in the form of tables and figures. We consider $581$ data's of observed values of distance modulus of various SNe Ia type supernovae from union $2.1$ compilation to compare our theoretical results with observations and found that model satisfies current observational constraints. We have also calculated the time and redshift at which acceleration in the Universe had commenced.