FRW type Kaluza–Klein modified holographic Ricci dark energy models in Brans–Dicke theory of gravitation

In this paper, we investigate non-Ricci, non-compact Friedmann–Robertson–Walker type Kaluza–Klein cosmology in the presence of pressureless matter and modified holographic Ricci dark energy in the frame work of Brans and Dicke (Phys Rev 124:965, 1961) scalar–tensor theory of gravitation. We solve the field equations of this theory using a hybrid expansion law for the five dimensional scale factor. We have also used a power law and a form of logarithmic function of the scale factor for the Brans–Dicke scalar field. Consequently, we obtain two interesting cosmological models of the Kaluza–Klein universe. We have evaluated the cosmological parameters, namely, the equation of state parameter, the deceleration parameter, and the density parameters. To check the stability of our models we use the squared speed of sound. Some well-known cosmological (ωde\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\omega _{de}$$\end{document}–ωde′\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\omega ^{\prime }_{de}$$\end{document} and statefinder) planes are constructed for our models. We have also analyzed the physical behavior of these parameters through graphical representation. It is observed that the FRW type Kaluza–Klein dark energy models presented are compatible with the present day cosmological observations.