Is dark energy necessary for the sustainability of traversable wormholes?

Dark energy is typically the principal component needed for the traversability of wormholes（WH）, as it provides the negative gravity effect required to keep the throat open. However, can this be achieved without dark energy? It turns out that if we couple the trace of energy-momentum with the standard Einstein-Hilbert Lagrangian and utilize a specific equation of state（EoS）, 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 EoS an ideal candidate for generating traversable WH geometries. The laboratory proven phenomenon provides a natural mechanism to sustain an open WH throat without relying on dark energy. Therefore, we generate two classes of WH solutions using 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 52, 2030（1995）] and different choices of redshift functions, we determine the WH geometry completely. The obtained WH solutions violate the NECs, and all qualitative constraints demanded for physically realizable WHs are satisfied. This is demonstrated via graphical plots for a suitably chosen range of coupling parameter values. Furthermore, our study investigates the repulsive effect of gravity, revealing that its presence leads to a negative deflection angle for photons traveling along null geodesics. Notably, we observe a consistent pattern of negative values for the deflection angle across all values of r0 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.