Granda-Oliveros dark energy in non-conserved gravity theory

Recently, reinvestigating Rastall idea T mu;nu nu=a,mu\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\mathcal{T}}}_{ \mu ;\nu }<^>\nu = a_{,\mu }$$\end{document} through relativistic thermodynamics proposed new non-conservation theory of gravity in which scalar parameter a,mu\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$a_{,\mu }$$\end{document} depends on 4-vector entropy S mu\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$S_\mu$$\end{document}, comoving temperature T0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$T_0$$\end{document} and density of charge of whole the system (Fazlollahi in Eur Phys J C 83:923, 2023). Considering this model deeply shows unlike other modified theories of gravity it cannot explain current phase of the Universe in absence of the cosmological constant and or other dark energy models. Hence, in this paper, by implementing the Granda-Oliveros infrared cut-off the late time evolution of the Universe is studied. As shown, for non-interaction scenario model yields same results given by Granda-Oliveros holographic dark energy in standard Einstein field equations. As result, the non-conservation term gives no tangible effects in this scenario. However, in interaction scenario one finds tangible effects of non-conservation term in evolution of dark energy which supports observations with some small errors in structure formation during matter dominated-era.