Wormhole Solutions and Pre-inflationary Epoch in $F(R, T)$ Gravity with Axion Fields

In this study, we investigate wormhole solutions within the framework of $F(R,T)$ gravity coupled to an axion-dilaton system and explore the inflation. Based on the Giddings-Strominger (GS) and expanding wormhole solutions in asymptotically flat Euclidean spacetime, the matter-geometry coupling term induces complex dynamical oscillations and reduces the Euclidean action, which enhances the nucleation probability of wormholes. Furthermore, we apply this theoretical setup to a "wineglass" half-wormhole model in Euclidean Anti-de Sitter (EAdS) spacetime and derive a constraint on the coupling parameter. This constraint introduces an unstable maximum in scalar potential, altering the probability distribution of initial states and the evolution of universes from high-potential regions. This method increases the probability of long-lasting inflation, offering a potential pathway to reconciling the no-boundary proposal with astronomical observations.