A look into the cosmological consequences of a dark energy model with higher derivatives of $H$ in the framework of Chameleon Brans-Dicke Cosmology

In this paper, we study some relevant cosmological features of a Dark Energy (DE) model with Granda-Oliveiros cut-off, which is just a specific case of Nojiri-Odintsov holographic DE unifying phantom inflation with late-time acceleration, in the framework of Chameleon Brans-Dicke (BD) Cosmology. Choosing a particular ansatz for some of the quantities involved, we derive the expressions of some important cosmological quantities, like the Equation of State (EoS) parameter of DE $w_D$, the effective EoS parameter $w_{eff}$, the pressure of DE $p_D$ and the deceleration parameter $q$. Moreover, we study the behavior of statefinder parameters $r$ and $s$, of the cosmographic parameters $j$, $s_{cosmo}$, $l$ and $m$ and of the squared speed of the sound $v_s^2$ for both case corresponding to non interacting and interacting Dark Sectors. We also plot the quantities we have derived and we calculate their values for $t\to 0$ (i.e. for the beginning of the Universe history), for $t\to \mathrm{\infty }$ (i.e. for far future) and for the present time, indicated with $t_0$. The EoS parameters have been tested against various observational values available in the literature.