  In this work we present a few simple cosmological models under the modified
theory of gravity in the particular form of
$f(R,\mathcal{T})=R+2f(\mathcal{T})$, where $R$ is the Ricci Scalar and
$\mathcal{T}$ is the trace of the energy-momentum tensor. Two special
cosmological models are studied with (i) hyperbolic scale factor and (ii)
specific form of the Hubble parameter. The models are observed to predict
relevant cosmological parameters closer to the observational values. Both the
models reduce to overlap with the $\Lambda$CDM model at late times. We have
discussed some interesting results related to wormhole solutions as evolved
from our model. The possible occurrence of Big Trip in wormholes for the models
are also discussed.
