In recent years there has been a growing interest in the field of Casimir wormhole. In classical general relativity (GR), it is known that the null energy condition (NEC) has to be violated to have a wormhole to be stable. The Casimir effect is an experimentally verified effect that is caused due to the vacuum field fluctuations in quantum field theory. Since the Casimir effect provides the negative energy density, thus this act as an ideal candidate for the exotic matter needed for the stability of the wormhole. In this paper, we study the Casimir effect on the wormhole geometry in modified symmetric teleparallel gravity or f(Q) gravity, where the non-metricity scalar Q drives the gravitation interaction. We consider three systems of the Casimir effect such as (i) two parallel plates, (ii) two parallel cylindrical plates, and (iii) two-sphere separated by a large distance to make it more experimentally feasible. Further, we studied the obtained wormhole solutions for each case with energy conditions at the wormhole throat with radius $$r_0$$r 0 and found that some arbitrary quantity violates the classical energy conditions at the wormhole throat. Furthermore, the behavior of the equation of state (EoS) is also analyzed for each case. Finally, we investigate the stability of the obtained Casimir effect wormhole solutions with the generalized Tolman–Oppenheimer–Volkoff (TOV) equation.

This article describes the study of wormhole solutions in $f\left(Q\right)$ gravity with noncommutative geometry. Here, we considered two different $f\left(Q\right)$ models—a linear model $f\left(Q\right)=\alpha Q$ and an exponential model $f\left(Q\right)=Q-\alpha \left(1-e^{-Q}\right)$, where Q is the non-metricity and $\alpha$ is the model parameter. In addition, we discussed the existence of wormhole solutions with the help of the Gaussian and Lorentzian distributions of these linear and exponential models. We investigated the feasible solutions and graphically analyzed the different properties of these models by taking appropriate values for the parameter. Moreover, we used the Tolman–Oppenheimer–Volkov (TOV) equation to check the stability of the wormhole solutions that we obtained. Hence, we found that the wormhole solutions obtained with our models are physically capable and stable.