Is dark energy necessary for the sustainability of traversable wormholes?

Abstract

Abstract Dark energy is usually the principal ingredient needed for traversability of wormholes by providing the negative gravity effect to keep the throat open. But can the same be achieved without dark energy? It turns out that if we couple the trace of energy-momentum with the standard Einstein-Hilbert Lagrangian and utilise a specific equation of state then dark energy may be obviated. The Casimir stress energy is known to result in the violation of the null energy condition (NEC) on the energy momentum tensor. This phenomenon makes such an equation of state (EoS) an ideal candidate to generate traversable wormhole (WH) geometries. The laboratory proven phenomenon provides a natural mechanism to sustain an open WH throat without having to appeal to dark energy. We generate two classes of WH solutions with this in energy-momentum trace-coupling gravity.
 For the specific choice of the Casimir EoS relating the energy-momentum tensor components [ Kar and Sahdev: Phys. Rev D {\bf 52} 2030 (1995)] and different choices for redshift functions, we determine the WH geometry completely. The obtained WH solutions violate the NECs and all qualitative constraints demanded of physically realisable WHs are satisfied. This is demonstrated via graphical plots for a suitably chosen range of values of the coupling parameter. Furthermore, our study involved an investigation into the repulsive effect of gravity, which revealed that its presence leads to a negative deflection angle for photons traveling along null geodesics. Notably, we observed a consistent pattern of negative values for the deflection angle across all values of $r_0$ in the three scenarios considered, thus indicating the clear manifestation of the repulsive gravity effect. All of this is possible without invoking the existence of dark energy.