The Lambert $W$ function: A newcomer in the Cosmology class?

TL;DR

This paper introduces a new cosmological model using a Lambert W function-based equation of state, successfully reproducing the Universe's evolution and suggesting perpetual late-time acceleration.

Contribution

It presents a novel equation of state incorporating the Lambert W function to model the Universe's evolution, a unique approach in cosmology.

Findings

Reproduces all evolutionary phases of the Universe.

Shows the initial singularity is unavoidable.

Predicts eternal late-time acceleration.

Abstract

We propose a novel equation of state (EoS) which explains the evolutionary history of a flat Friedmann-Lemaitre-Robertson-Walker (FLRW) Universe. The uniqueness of this EoS lies in the fact that it incorporates the Lambert $W$ function in a special fashion. It is explicitly demonstrated that with observationally relevant values of the unknown parameters $\vartheta_\mathrm{1}$ and $\vartheta_\mathrm{2}$, all the evolutionary phases of the Universe can be reproduced. Moreover, it also shows that the initial singularity is unavoidable and asserts that the late-time acceleration of the Universe would continue forever.