Role of cosmic voids and their matter properties in shaping wormhole geometry in generalized geometry-matter coupling gravity

Cosmic voids are increasingly recognized as a promising tool for cosmological exploration. Their distribution and density profiles are highly responsive to alterations in gravitational theories, along with the influences of dark energy and neutrinos. Investigating voids offers a compelling opportunity to uncover signatures of alternative gravity models on a cosmological level. Voids span a notable range of density contrasts, from approximately -$1$ near their centers to around $0$ at their edges, where screening mechanisms become less effective. The primary objective of this study is to explore a novel model that introduces a new category of wormhole solutions by leveraging cosmic voids$-$vast underdense regions of the universe$-$for the first time. We focus on identifying new exact static wormhole models by proposing an alternative viewpoint on their matter content, rooted in the recently formulated $f(R,\mathcal{L}_m,T)$ theory of gravity. By developing a unique solution based on a universal density profile for voids, we examine crucial constraints on the parameters that dictate matter distribution and the structure of spacetime itself. Our results reveal how these cosmic voids significantly influence the geometry of wormholes, steepening the gradient toward the throat and mitigating violations of the null and weak energy conditions, particularly beyond their centers. We also highlight intriguing gravitational lensing effects, showing that this wormhole repels light rather than capturing it, creating a fascinating interaction between gravity and light.