A complete theory of gravity impels us to go beyond Einstein’s general relativity. One promising approach lies in a new class of teleparallel theory of gravity named $f(Q)$, where the nonmetricity $Q$ is responsible for the gravitational interaction. The important roles any of these alternative theories should obey are the energy condition constraints. Such constraints establish the compatibility of a given theory with the causal and geodesic structure of space-time. In this work, we present a complete test of energy conditions for $f(Q)$ gravity models. The energy conditions allowed us to fix our free parameters, restricting the families of $f(Q)$ models compatible with the accelerated expansion our Universe passes through. Our results strengthen the viability of $f(Q)$ theory, leading us close to the dawn of a complete theory for gravitation.

Recent elaborated by Harko et al., the f(R, T) theories of gravity allow one to contemplate an optimistic alternative to dark energy, for which R

An intriguing solution that appears in General Relativity (GR) but has not been observed so far is the wormhole. This exotic solution describes a topological bridge connecting two distinct universes or two different points in the same universe. It is known that the traversable wormhole solutions violate all the energy conditions in GR, resulting in their instability. In this work, we are going to unveil new wormhole solutions for f(Q) gravity where Q is the nonmetricity scalar, which is responsible for the gravitational interaction. The energy conditions to constraint these wormhole solutions were derived using the embedding procedure. This procedure consists in rewriting the density and the pressures of the solutions as those presented by General Relativity. Then, the nontrivial contributions coming from new theories of gravity are embedded into the effective equations for density and pressures. Along with our approach, we carefully analyze two families of f(Q) models and we use two different shape functions to build the wormholes solutions for each of these f(Q) models. We are going to present new scenarios with the possibility of traversable wormholes satisfying SEC or DEC energy conditions in the presence of exotic matter.