Time-Dependent Wormhole Solutions of $f(R)$ Theory of Gravity and Energy Conditions

Abstract: In this work, we construct time-dependent wormhole solutions in the context of $f(R)$ theory of gravity. The background matter is considered to be traceless. By considering specific shape function and power-law expansion exact solutions for $f(R)$ are found. The null and the weak energy conditions (NEC and WEC) are checked for wormhole solutions. It is shown that the matter threading the wormhole spacetimes with either accelerated expansion or decelerated expansion satisfies the NEC and WEC.