Wormholes in 4D Einstein-Gauss-Bonnet gravity with BEC Dark Matter density profile

Abstract

The existence of Traversable Wormhole (TW) in the 4D Einstein-Gauss-Bonnet (4D-EGB) gravity is explored with phenomenological Bose-Einstein Condensates (BEC) dark matter density profile. In the framework of 4D EGB gravity, which one obtains by regularizing the higher-dimensional EGB gravity in the limit $D \to 4$ is considered to obtain a spherically symmetric TW. The Gauss-Bonnet coupling parameter ($\alpha$) in this case is rescaled to $\alpha \to \frac{\alpha}{D-4}$. Considering the energy density profile of non-relativistic BEC matter, the shape function of the WH geometry and the Null energy condition (NEC) are determined with a constant redshift function. The applicability of realistic flaring-out condition and asymptotic flatness conditions are studied here and the domain of model parameters for realistic scenario is determined. We analyze the embedding diagram of the WH obtained here with proper radial distance, volume integral quantifier, and anisotropy. We obtained WH which is stable at the throat when $\alpha = -0.0512471$ for a set of model parameters, which is estimated from sound speed measurement. The energy conditions are investigated, and it is noted that there is a range of Gauss-Bonnet coupling parameter $\alpha \in [-4,-4.222]$, at which the energy conditions, including NEC, are obeyed at the throat. We explore NEC for other values of $\alpha$ and found that it is not satisfied. The other energy conditions are also violated. A new result is thus obtained with 4D Einstein-Gauss-Bonnet gravity with BEC Dark Matter profile. We determine the parameter space for which the WH solution exists in the proposed modified gravity model.