Evolving Wormholes in a Cosmological Background

Abstract

Wormholes are non-trivial topological structures that arise as exact solutions to Einstein's field equations, theoretically connecting distinct regions of spacetime via a throat-like geometry. While static traversable wormholes necessarily require exotic matter that violates the classical energy conditions, subsequent studies have sought to minimize such violations by introducing time-dependent geometries embedded within cosmological backgrounds. This review provides a comprehensive survey of evolving wormhole solutions, emphasizing their formulation within both general relativity and alternative theories of gravity. We explore key developments in the construction of non-static wormhole spacetimes, including those conformally related to static solutions, as well as dynamically evolving geometries influenced by scalar fields. Particular attention is given to the wormholes embedded into Friedmann-Lemaître-Robertson-Walker (FLRW) universes and de Sitter backgrounds, where the interplay between the cosmic expansion and wormhole dynamics is analyzed. We also examine the role of modified gravity theories, especially in hybrid metric-Palatini gravity, which enable the realization of traversable wormholes supported by effective stress-energy tensors that do not violate the null or weak energy conditions. By systematically analyzing a wide range of time-dependent wormhole solutions, this review identifies the specific geometric and physical conditions under which wormholes can evolve consistently with the null and weak energy conditions. These findings clarify how such configurations can be naturally integrated into cosmological models governed by general relativity or modified gravity, thereby contributing to a deeper theoretical understanding of localized spacetime structures in an expanding universe.

23 pages, 4 figures. Invited contribution to the Universe Special Issue "Experimental and Observational Constraints on Wormhole Models"

References in corpus (34)

• Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models
• Palatini Approach to Modified Gravity: f(R) Theories and Beyond
• Wormhole geometries in f(R) modified theories of gravity
• Inflationary cosmology in modified gravity theories
• Modified-gravity wormholes without exotic matter
• Solar system and equivalence principle constraints on f(R) gravity by chameleon approach
• Wormholes supported by hybrid metric-Palatini gravity
• Modelling wormholes in $f(R,T)$ gravity
• Wormhole geometries supported by a nonminimal curvature-matter coupling
• Static Spherically Symmetric Wormholes in $f(R,T)$ Gravity
• Nonminimal curvature-matter coupled wormholes with matter satisfying the null energy condition
• Wormholes in viable $f(R)$ modified theories of gravity and Weak Energy Condition
• Non-exotic matter wormholes in a trace of the energy-momentum tensor squared gravity
• Cosmology of hybrid metric-Palatini f(X)-gravity
• General class of wormhole geometries in conformal Weyl gravity
• Charged spherically symmetric black holes in $f(R)$ gravity and their stability analysis
• Evolving wormhole geometries within nonlinear electrodynamics
• Higher-dimensional evolving wormholes satisfying the null energy condition
• Traversable Wormholes in $R+\alpha R^n$ Gravity
• Traversable wormholes in $f(R)$ gravity with constant and variable redshift functions
• N-dimensional static and evolving Lorentzian wormholes with cosmological constant
• Evolving Lorentzian wormholes supported by phantom matter and cosmological constant
• Static traversable wormhole solutions in $f(R,L_m)$ gravity
• Dynamics of Linear Perturbations in the hybrid metric-Palatini gravity
• Evolving Lorentzian wormholes supported by phantom matter with constant state parameters
• Dynamic wormhole solutions in Einstein-Cartan gravity
• Dynamic wormhole geometries in hybrid metric-Palatini gravity
• Dynamic wormholes with particle creation mechanism
• Evolving wormhole in the brane-world scenario
• Non-exotic traversable wormholes in $f\left(R,T_{ab}{T}^{ab}\right)$ gravity
• Estimating the parameters of Hybrid Palatini gravity model with the Schwarzschild precession of S2, S38 and S55 stars: case of bulk mass distribution
• Role of higher -dimensional evolving wormholes in the formation of a big rip singularity
• Dynamics and Thermodynamics of (2+1)-Dimensional Evolving Lorentzian Wormhole
• Lorentzian Wormholes in the Friedman-Robertson-Walker Universe

Cited by in corpus (1)

• Analytical solution of traversable wormholes in the presence of positive cosmological constant