We propose, as a novelty in the literature, the modeling of wormholes within a particular case of f (R, T ) gravity, namely f (R, T ) = R + α R 2 + λT , with R and T being the Ricci scalar and trace of the energy-momentum tensor, respectively, while α and λ are constants. Although such a functional form application can be found in the literature, those concern compact astrophysical objects, such that no wormhole analysis has been done so far. The quadratic geometric and linear material corrections of this theory render the matter content of the wormhole remarkably able to obey the energy conditions.

The objective of this work enclosed with the study of spatially homogeneous anisotropic Bianchi type-I universe in f (R, T ) gravity (where R is the Ricci scalar and T is the trace of stress energy momentum tensor) in two different cases viz. f (R, T ) = R + 2f (T ) and f (R, T ) = f 1 (R) + f 2 (T ) with bulk viscosity matter content. In this study, we consider a time varying deceleration parameter, which generates an accelerating universe to obtain the exact solution of the field equations. The physical and kinematical properties of both the models are discussed in detail for the future evolution of the universe. We have explored the nature of WEC, DEC, SEC and energy density for both the cases. We have found that both the models, with bulk viscosity matter component, show an acceleration of the universe. We have also shown that the cosmic jerk parameter is compatible with the three kinematical data sets.

Wormholes are tunnels connecting different regions in space-time. They were obtained originally as a solution for Einstein's General Relativity theory and according to this theory they need to be filled by an exotic kind of anisotropic matter. In the present sense, by "exotic matter" we mean matter that does not satisfy the energy conditions. In this article we propose the modelling of wormholes within an alternative gravity theory that proposes an extra material (rather than geometrical) term in its gravitational action. Our solutions are obtained from well-known particular cases of the wormhole metric potentials, named redshift and shape functions, and yield the wormholes to be filled by a phantom fluid, that is, a fluid with equation of state parameter ω < −1. In possession of the solutions for the wormhole material content, we also apply the energy conditions to them. The features of those are carefully discussed.