Because the null energy conditions (NECs) are violated in both cases, an amazing and unexpected overlap occurs between these two seemingly separated subjects. More recently, as demonstrated in our previous works [@39; @40; @41; @42], we are dedicated to investigating the related properties and features of wormhole space–time structure for a given dynamical dark energy scenario. In the present study, we explore traversable wormholes in the framework of MOG. As a concrete case, traversable wormholes supported by astrophysical observations in the DGP scenario are investigated. In what follows, it is very necessary to provide a brief historical review on wormholes.

The first study of wormhole physics can be traced back to Flamm in 1916, when he analyzed the newly discovered Schwarzschild solution [@43]. Subsequently, in 1935, Einstein and Rosen (ER) proposed the so-called ER bridge when they attempted to construct a geometrical model for a physical fundamental particle, e.g., an electron [@44]. After the pioneering study by ER, this field lay dormant for almost two decades. Then, in 1955, Wheeler developed the appealing concept of a “geon, ” which was assumed to be the solution of the coupled Einstein–Maxwell equation [@45]. From the point of view of topology, he considered 