Semi-classical treatment of $k$-essence effect on cosmic temperature

TL;DR

This paper presents a semi-classical model incorporating a $k$-essence scalar field to explain the evolution of the Cosmic Microwave Background Radiation, successfully matching key observational features and highlighting the role of inhomogeneity in cosmic acceleration.

Contribution

It introduces a phenomenological $k$-essence based model that captures observed cosmic acceleration features and explores the impact of inhomogeneity on the universe's expansion history.

Findings

Model reproduces observed transition from deceleration to acceleration.

Inhomogeneity parameter influences the epoch of acceleration.

Negative inhomogeneity parameter aligns better with observations.

Abstract

A phenomenological model is described for Cosmic Microwave Background Radiation (CMBR) evolution with dark energy an essential ingredient in the form of a $k-$essence scalar field. The following features of this evolution can be successfully obtained from this model: (a) the {\it observed} variation of the rate of change of scale factor $a(t)$, i.e. $\dot a$, with time and (b) the {\it observed} value of the epoch when the universe went from a decelerating phase to an accelerated phase. These two features have been matched with graphical transcriptions of SNe Ia data. The model also indicates that the evolution is sensitive to the presence of inhomogeneity and this sensitivity increases as one goes further into the past. Further, the value of the inhomogeneity parameter determines the epoch of switch over to an accelerated phase. A positive value of inhomogeneity parameter leads to switch over at earlier epochs, while a negative value leads to switch over at later epochs. If the value of the inhomogeneity parameter is a bit negative then the crossover point from deceleration to acceleration gives better agreement with the observed value.