Comprehensive Study of $k$-essence Model: Dynamical System Analysis and Observational Constraints from Latest Type Ia Supernova and BAO Observations

TL;DR

This paper constrains $k$-essence scalar field models with inverse square and exponential potentials using recent observational data, analyzing their dynamical evolution, stability, and comparing their fit to the standard $\\Lambda$CDM model.

Contribution

It provides a comprehensive observational and dynamical analysis of $k$-essence models, including stability constraints and Bayesian parameter estimation, comparing their performance to $\\Lambda$CDM.

Findings

$k$-essence models fit observational data well.

$\\Lambda$CDM model has a slightly better Bayesian Information Criterion score.

Stability constraints inform prior choices for model parameters.

Abstract

We constrain the parameters of the $k$-essence scalar field model with inverse square and exponential potentials using data sets including Pantheon+SHOES and the Dark Energy Survey (DES) of Type Ia supernovae, Baryon Acoustic Oscillation (BAO) data from SDSS and DESI surveys, and direct measurements of the Hubble parameter and redshift obtained from the differential age method (CC). We also provide a brief perspective on the dynamical evolution of both models and derive stability constraints on the model parameters, which are then used to set appropriate priors. We adopt a Bayesian inference procedure to estimate the model parameters that best fit the data. A comprehensive analysis in light of observational data shows that the $k$-essence model fits well across all data combinations. However, according to the BIC criterion, the $\Lambda$CDM model provides a slightly better fit compared to the $k$-essence model.