Wormhole spacetimes in an expanding universe: Energy conditions and future singularities

TL;DR

This paper explores wormhole geometries in an expanding universe using a four-scalar non-linear sigma model, showing how energy conditions can be satisfied and revealing novel geometries with future singularities and connections to dark matter profiles.

Contribution

It introduces a framework where wormholes remain stable despite energy condition violations and demonstrates how cosmological expansion modifies these conditions.

Findings

Wormholes can be stable even when energy conditions are violated.

Cosmological expansion allows energy conditions to be satisfied.

New geometries with future singularities connecting different universes.

Abstract

We study wormhole geometries embedded in an expanding universe within a four-scalar non-linear $\sigma$ model, where the target-space metric is identified with the spacetime Ricci tensor. In this framework, wormholes can remain stable even when conventional energy conditions are violated. However, once cosmological expansion is included, the effective energy density and pressure are modified by the cosmological fluid, enabling the energy conditions to be satisfied. We further present intriguing geometries in which a finite future singularity appears in our universe but not in another universe connected by the wormhole. Near the throat, the hypersurface becomes timelike, allowing trajectories to traverse to the other universe before the singularity and return afterwards. We also construct wormhole solutions motivated by galactic dark-matter halo profiles, where the required non-vanishing pressure arises naturally from the four-scalar non-linear $\sigma$ model.