  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.
