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 $n=\pm 1\mathrm{/}2$, 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 $n=-1\mathrm{/}2$ 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.