Evolving topologically deformed wormholes supported in the dark matter halo

In this paper, we construct an evolving wormhole in the dark matter halo. This work is relevant since matter has two components: (i) cosmological part (only time-dependent) and (ii) wormhole part (only space-dependent). In order to implement this, we use the Chaplygin gas as an equation of state for the cosmic part and Navarro-Frenk-White dark matter density profile as well as Thomas-Fermi (TF) profile in order to form a dark wormhole. The flare-out condition of wormhole is also satisfied by violating the null energy condition (NEC) for some specific values of quantities. Furthermore, we reveal more interesting results regarding how an topologically deformation parameter $\alpha$ affects the evolving wormhole sourced with some dark matter models based on the physically motivated shape function.