Bayesian model selection on Scalar $\epsilon$-Field Dark Energy

The main aim of this paper is to analyse minimally-coupled scalar-fields -- quintessence and phantom -- as the main candidates to explain the accelerated expansion of the universe and compare its observables to current cosmological observations; as a byproduct we present its python module. This work includes a parameter $\epsilon$ which allows to incorporate both quintessence and phantom fields within the same analysis. Examples of the potentials, so far included, are $V(\phi)=V_0\phi^{\mu}e^{\beta \phi^\alpha}$ and $V(\phi)=V_0(\cosh(\alpha \phi)+\beta)$ with $\alpha$, $\mu$ and $\beta$ being free parameters, but the analysis can be easily extended to any other scalar field potential. Additional to the field component and the standard content of matter, the study also incorporates the contribution from spatial curvature ($\Omega_k$), as it has been the focus in recent studies. The analysis contains the most up-to-date datasets along with a nested sampler to produce posterior distributions along with the Bayesian evidence, that allows to perform a model selection. In this work we constrain the parameter-space describing the two generic potentials, and among several combinations, we found that the best-fit to current datasets is given by a model slightly favouring the quintessence field with potential $V(\phi)=V_0\phi^\mu e^{\beta \phi}$ with $\beta=0.22\pm 1.56$, $\mu = -0.41\pm 1.90$, and slightly negative curvature $\Omega_{k,0}=-0.0016\pm0.0018$, which presents deviations of $1.6\sigma$ from the standard $\Lambda$CDM model. Even though this potential contains three extra parameters, the Bayesian evidence $\mathcal{B}_{\Lambda, \phi} =2.0$ is unable to distinguish this model compared to the $\Lambda$CDM with curvature ($\Omega_{k,0}=0.0013\pm0.0018$). The potential that provides the minimal Bayesian evidence corresponds to $V(\phi)=V_0 \cosh(\alpha \phi)$ with $\alpha=-0.61\pm 1.36$.