Simple-graduated dark energy and spatial curvature

TL;DR

This paper explores minimal extensions to the $ ext{Lambda}$CDM model, including spatial curvature and simple-graduated dark energy, to address tensions in $H_0$ and BAO data, finding limited deviations from standard cosmology.

Contribution

It introduces and analyzes simple-graduated dark energy and spatial curvature as potential solutions to cosmological tensions, with detailed observational and dynamical assessments.

Findings

Models without Planck data show deviations from $ ext{Lambda}$CDM.

Spatially closed universe with positive inertial mass density slightly reduces $H_0$ tension.

Including Planck data, models align closely with $ ext{Lambda}$CDM, offering minimal improvements.

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-$\alpha$ data, both which prevail within the $\Lambda$CDM model. We then investigate whether two minimal extensions of the $\Lambda$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 $\Lambda$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 $\mathcal{O}(10^{-12})\,\rm eV^4$. The latter case predicts almost no deviation from the $\Lambda$CDM model up until today--so that it results in no improvement regarding the BAO Ly-$\alpha$ 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 $\Lambda$CDM model.