$w=p/\rho=-1$ (with $p$ and $\rho$ being the fluid pressure and energy density). However, one should note that the $\Lambda$CDM model, although providing a reasonable fit to most observational constraints, is still confronted with the well-known coincidence problem and fine-tuning problem [@Weinberg]. See @Cao11a [@Cao14] and references therein for recent discussions about more dark energy models under discussion [@Cao11b; @Cao13; @Cao15a; @Qi18] .

On the other hand, dark energy is not the only possible explanation of the present cosmic acceleration, and it is argued that the observed accelerated expansion should instead be viewed as the possible deviation from Einstein’s theory of gravity on large cosmological length scales. For instance, some unknown physical processes involving modifications of gravity theory can also account for this apparently unusual phenomenon. Some modifications are related to the possible existence of extra dimensions, which gives rise to the so-called braneworld cosmology. In this paper we investigate constraints on one interesting braneworld cosmological model proposed by @Dvali00a [@Arkani; @Dvali00b], the Dvali-Gabadadze-Porrati (DGP) braneworld, which is often used to describe a gravity spilling over large scales and into higher dimensions. So far, both models derived from introducing an exotic component like dark energy and those established by modifying Einstein’s 