explore the relationships between the structure formation of traversable wormholes and energy conditions from the point of view of cosmology. Furthermore, we exhibit these underlying relations by using the DGP braneworld scenario in the framework of MOG. Substituting Eq. (\[8\]) into different conditional inequalities ([@19; @20; @21; @22]), we find that the model parameter ($\alpha$, $\beta$) and redshift $z$ will enter the energy conditions and affect the structure formation of traversable wormholes. More precisely, the WEC and DEC are automatically satisfied in the possible range \[0.2874, *z*\], where *z* represents the possible value of the low redshift (see Fig. \[f6\]). Note that we investigated the energy conditions in terms of the $2\sigma$ confidence level. In addition, we can easily find that the second inequality $\rho+3p\geqslant0$ of the SEC is always violated at low redshifts.

More physically, the DEC implies that the dark energy fluid cannot travel faster than the speed of light and that the nonviolation of the WEC indicates that the dark energy fluid in the DGP scenario has a nondiverging effect on congruences of null geodesics. Meanwhile, the SEC provides a tighter limitation than the WEC but it is still physically reasonable for the stress–energy tensor. In the 