from the $M$ theory. More concretely, the accelerated universe could be the result of gravitational leakage into extra dimensions over Hubble distances rather than the consequence of a nonzero cosmological constant [@a3]. In the present situation, we just take into account the simplest braneworld scenario where the four-dimensional gravity on the brane is modified at low energies, becoming five-dimensional Dvali–Gabadadze–Porrati (DGP) scenarios, which is one class of the five-dimensional braneworld scenarios based on the Randall–Sundrum (RS) scenarios.

As in our previous works [@39; @40; @41; @42], the present study is aimed at exploring the astrophysical scale properties of the braneworld scenario by assuming that the dark energy fluid permeates over the whole universe. More precisely, we investigate the properties and features of a mysterious astrophysical object, i.e., a wormhole, which has attracted considerable attention today along with other astrophysical objects, such as pulsars, white dwarfs, and black holes.

Wormholes can be defined as a class of special space–time structure connecting two different universes or two widely separated regions of our own universe. In recent years, gradually mounting interest in the subject is mainly ascribed to the stirring and elegant discovery that the universe is experiencing a phase of accelerated expansion. 