Scalar Field Dominated Cosmology with Woods-Saxon Like Potential

Dark energy can be characterized by a canonical scalar field, known as quintessence. Quintessence allows for a dynamical equation of state -1 ≤ ω ≤ -1/3. In this work, we consider a quintessence model with a specific potential of the Woods-Saxon form. 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 H₀ = 68.10 ± 0.74\,km s⁻¹ Mpc⁻¹ and the matter energy density parameter Ωm₀ = 0.31 ± 0.01, which are consistent with the values obtained using base ΛCDM using the same dataset. Computation of the χ²ₘᵢₙ, AIC and BIC reveal that this model is preffered according to AIC and χ²ₘᵢₙ criteria, while the ΛCDM is preferred according to BIC. We also show that this model can explain late-time accelerated expansion. Statefinder analysis reveals a Chaplygin gas behaviour in the past, in addition to the quintessence behaviour of the field.