Existence of non-exotic traversable wormholes in squared trace extended gravity theory

An extended gravity theory is used to explore the possibility of non-exotic matter traversable wormholes. In the extended gravity theory, additional terms linear and quadratic in the trace of the energy momentum tensor are considered in the Einstein-Hilbert action. Obviously, such an addition leads to violation of the energy-momentum tensor. The model parameters are constrained from the structure of the field equations. Non-exotic matter wormholes tend to satisfy the null energy conditions. We use two different traversable wormhole geometries namely an exponential and a power law shape functions to model the wormholes. From a detailed analysis of the energy conditions, it is found that, the existence of non-exotic matter traversable wormholes is not obvious in the model considered and its possibility may depend on the choice of the wormhole geometry. Also, we found that, non-exotic wormholes are possible within the given squared trace extended gravity theory for a narrow range of the chosen equation of state parameter.