Nonlinear matter terms in general scalar-tensor braneworld cosmology

A five dimensional braneworld cosmological model in general scalar-tensor action comprises of various Horndeski Lagrangian is considered. The Friedmann equations in the case of the strongly and weakly coupled $\mathcal{L}_5$ Horndeski Lagrangian have been obtained. The strongly coupled $\mathcal{L}_5$ model produces the Cardassian term $\rho^n$ with $n=\pm 1/2$, which can served as alternative explanation for the accelerated expansion phase of the universe. Furthermore, the latest combined observational facts from BAO, CMB, SNIa, $f_{\sigma_8}$, and $H_0$ value observation suggest that the $n=-1/2$ term lies quite close to the constrained value. On the other hand, the weakly coupled $\mathcal{L}_5$ case has several new correction terms which are omitted in the braneworld Einstein-Hilbert model, e.g. the cubic $\rho^3$ and the dark radiation-matter interaction term $\chi a^{-4}\rho$. Furthermore, this model provides a cosmological constant constructed from the bulk scalar field, requires no brane tension, and supports the big bang nucleosynthesis (BBN) constraint naturally.