Spherically symmetric solutions for f (T ) gravity models are derived by the so called Noether Symmetry Approach. First, we present a full set of Noether symmetries for some minisuperspace models. Then, we compute analytical solutions and find that spherically symmetric solutions in f (T ) gravity can be recast in terms of Schwarzschild-like solutions modified by a distortion function depending on a characteristic radius. The obtained solutions are more general than those obtained by the usual solution methods.

We consider Noether symmetry approach to find out exact cosmological solutions in f (T )-gravity. Instead of taking into account phenomenological models, we apply the Noether symmetry to the f (T ) gravity. As a result, the presence of such symmetries selects viable models and allow to solve the equations of motion. We show that the generated f (T ) leads to a power law expansion for the cosmological scale factor.

Modified gravity is one of the most favorable candidates for explaining the current accelerating expansion of the Universe. In this regard, we study the viability of an alternative gravitational theory, namely f (R, G), by imposing energy conditions. We consider two forms of f (R, G), commonly discussed in the literature, which account for the stability of cosmological solutions. We construct the inequalities obtained by energy conditions and specifically apply the weak energy condition using the recent estimated values of the Hubble, deceleration, jerk and snap parameters to probe the viability of the above-mentioned forms of f (R, G).

The equivalence between f (R) gravity and scalar-tensor theories is invoked to study the null, strong, weak and dominant energy conditions in Brans-Dicke theory. We consider the validity of the energy conditions in Brans-Dicke theory by invoking the energy conditions derived from a generic f (R) theory. The parameters involved are shown to be consistent with an accelerated expanding universe.