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 straight the viability of f (Q) theory, leading us close to the dawn of a complete theory for gravitation.

No abstract

The current interests in the universe motivate us to go beyond Einstein's General theory of relativity. One of the interesting proposals comes from a new class of teleparallel gravity named symmetric teleparallel gravity, i.e., f(Q) gravity, where the non‐metricity term Q is accountable for fundamental interaction. These alternative modified theories of gravity's vital role are to deal with the recent interests and to present a realistic cosmological model. This manuscript's main objective is to study the traversable wormhole geometries in f(Q) gravity. We construct the wormhole geometries for three cases: (i) by assuming a relation between the radial and lateral pressure, (ii) considering phantom energy equation of state (EoS), and (iii) for a specific shape function in the fundamental interaction of gravity (i.e. for linear form of f(Q)). Besides, we discuss two wormhole geometries for a general case of f(Q) with two specific shape functions. Then, we discuss the viability of shape functions and the stability analysis of the wormhole solutions for each case. We have found that the null energy condition (NEC) violates each wormhole model which concluded that our outcomes are realistic and stable. Finally, we discuss the embedding diagrams and volume integral quantifier to have a complete view of wormhole geometries.