Simple-graduated dark energy and spatial curvature

Abstract

In this work, we first discuss the possibility that dark energy models with negative energy density values in the past can alleviate the ${H}_{0}$ tension, as well as the discrepancy with the baryon acoustic oscillation (BAO) Lyman-$\ensuremath{\alpha}$ data, both which prevail within the $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ model. We then investigate whether two minimal extensions of the $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ model, together or separately, can successfully realize such a scenario: (i) the spatial curvature, which, in the case of spatially closed universe, mimics a negative density source and (ii) simple-graduated dark energy (gDE), which promotes the null inertial mass density of the usual vacuum energy to an arbitrary constant---if negative, the corresponding energy density decreases with redshift similar to the phantom models, but unlike them crosses below zero at a certain redshift. We find that, when the Planck data are not included in the observational analysis, the models with simple-gDE predict interesting and some significant deviations from the $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ model. In particular, a spatially closed universe along with a simple-gDE of positive inertial mass density, which work in contrast to each other, results in minor improvement to the ${H}_{0}$ tension. The joint dataset, including the Planck data, presents no evidence for a deviation from spatial flatness but almost the same evidence for a cosmological constant and the simple-gDE with an inertial mass density of order $\mathcal{O}({10}^{\ensuremath{-}12})\text{ }\text{ }{\mathrm{eV}}^{4}$. The latter case predicts almost no deviation from the $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ model up until today---so that it results in no improvement regarding the BAO Ly-$\ensuremath{\alpha}$ data---except that it slightly aggravates the ${H}_{0}$ tension. We also study via dynamical analysis the history of the Universe in the models, as the simple-gDE results in futures different than the de Sitter future of the $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ model.

Topics & Concepts