Study of Wormhole in $f(Q)$ gravity with some dark energy models

Abstract: This study discusses the development of some particular static wormhole models in the background of an extended $f(Q)$ gravity theory. Wormhole solutions are derived by considering the radial pressure to admit an equation of state corresponding to Chaplygin gas. The Chaplygin gas equation of state is taken into consideration in two different forms: $p_{r}=-\frac{Bb(r)^{u}}{\rho^{a}}$, $p_{r}=-\frac{B}{\rho^{a}}$. Wormhole models are also generated assuming that a variable barotropic fluid may explain the radial pressure given by $p_{r} =-\omega\rho b(r)^u$. For every model, the shape function $b(r)$ is the function that can be derived from the wormhole metric in any scenario. The stability analysis of the wormhole solutions and the shape function viability for each situation are then investigated.Since each wormhole model is shown to violate the null energy condition (NEC), it can be understood that these wormholes are traversable. More generally, we investigate whether the model is stable under the hydrostatic equilibrium state condition using the TOV equation.The physical characteristics of these models are shown under the same energy circumstances. The typical characteristic is the radial pressure $p_{r}$ near the wormhole throat, which violates the NEC $(\rho+P_{r} \geq0)$. In some models, it is possible to meet the NEC at the neck and yet violate the DEC $(\rho - P_{r}\geq0)$. In summary, precise wormhole models may be generated, provided that $(\rho\geq0)$, and there may be a potential breach of the NEC at the wormhole's throat.