Holographic Ricci dark energy in nonconservative unimodular gravity

Abstract

The structure of unimodular gravity (UG) is invariant to a subclass of diffeomorphism, the transverse diffeomorphism, due to the unimodular condition -g=ϵ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sqrt{-g}=\\epsilon $$\\end{document}. Consequently, there is a freedom to define how the conservation laws of the energy–momentum tensor in unimodular gravity in the cosmological context. One of the main characteristics of the complete system of equations that describe cosmological dynamics in UG is that they form an underdetermined system if the usual conservation law of the energy–momentum tensor is not considered in your structure. In this article, we propose the construction of a background cosmological model based on the description of a holographic dark energy component with a cutoff of the order of Ricci scalar in non-conservative UG. This choice means that the complete set of equations remains underdetermined, however, the new feature of this cosmological model is the appearance of an interaction between matter and dark energy. Indeed, this is a well-known characteristic of cosmological models in which we have holographic dark energy density. Consequently, we propose an ansatz to the interaction term Q=βHρm\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$Q=\\beta H \\rho _{m}$$\\end{document}, and obtain the cosmological parameters of our model. We found a viable universe model with similar characteristics to the ΛCDM\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Lambda \ extrm{CDM}$$\\end{document} model. We performed statistical analysis of the background model using the “Cosmic Chronometer” (CC) data for H(z), and obtain as a result using AIC, and the BIC as model selection criteria that ΛCDM\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Lambda \ extrm{CDM}$$\\end{document} prevails as the best model. However, the proposed model is competitive when compared to the cosmological model ωCDM\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\omega \ extrm{CDM}$$\\end{document}.