Scalar Field Dominated Cosmology with Woods-Saxon Like Potential

Abstract: Dark energy can be characterized by a canonical scalar field, known as quintessence. Quintessence allows for a dynamical equation of state $-1 \le \omega \le -\frac{1}{3}$. A previous study by Oikonomou and Chatzarakis have shown that a scalar field model with a Woods-Saxon like potential can successfully explain the early inflation. In this work, we consider a quintessence model with a potential of similar form to explain the late time acceleration. The model is studied at late phase assuming flat cosmology, and the model parameters are constrained using Type Ia supernova data and Observational Hubble data. In particular we employ Markov Chain Monte Carlo methods for the Bayesian inference of these parameters. We obtain the value of the Hubble constant $H_0 \sim 68 \text{ km s}^{-1} \text{Mpc}^{-1}$ and the matter energy density parameter $\Omega_{m_0} \sim 0.30 $, which are in close agreement with the values obtained from the Planck CMB data, assuming the $\Lambda$CDM model. Computation of the $\chi^2_{min}$, AIC and BIC reveal that this model is slightly preferred according to AIC and $\chi^2_{min}$ criteria, while the $\Lambda$CDM is preferred according to BIC. We demonstrate that the model possesses a stable attractor in the asymptotic future, which confirms the dynamical stability of the model. Thus, this model may be considered as a potential alternative to the $\Lambda$CDM.