Holographic dark energy inflation model in modified f(R,G) gravitational framework

In the present analysis, we have constructed the Friedmann-Lemaitre-Robertson-Walker (FLRW) cosmological model of the universe by choosing the source as Holographic and Renyi holographic dark energy. The holographic and Renyi holographic dark energy fluids have shown their dominance towards Hubble’s and Granda-Oliveros cut-off in the context of modified gravity say f(R, G) gravity, where R be the Ricci scalar and G be the Gauss-Bonnet invariant. We investigate the properties of the resulting cosmological model using the relation between H and a as H=baη\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$H=ba^{\eta }$$\end{document} which omit the volumetric power law expansion of the form a=(ηbt+b1)1η\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$a=(\eta b t + b_{1})^{\frac{1}{\eta }}$$\end{document}, where η≥0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\eta \ge 0$$\end{document}, b>0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$b >0$$\end{document} are constants, and b1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$b_{1}$$\end{document} is an integrating constant. The scale factor that simulates the accelerating expansion with 0≤q≤-1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$0 \le q \le -1$$\end{document} equivalent to q=-0.45\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$q=-0.45$$\end{document}. The physical parameters of the model such as energy density, equation of state parameter, squared velocity of sound with redshift are also derived and analyzed.