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Evolving Wormholes in a Cosmological Background

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Mahdi Kord Zangeneh, Francisco S. N. Lobo

General Relativity and Quantum Cosmology · Submitted 19 Jul 2025 · 103 references

Pith's verdict: A competent review of evolving wormholes that usefully consolidates the literature, but the authors' strongest claim—that their hybrid metric-Palatini wormhole satisfies NEC/WEC at all times—is only supported over a finite redshift window and needs an asymptotic check.

T0 · AI review

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arXiv ID2507.14750 (version 1)
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CitationFrancisco S. N. Lobo, Mahdi Kord Zangeneh. "Evolving Wormholes in a Cosmological Background." arXiv:2507.14750 (2025). https://pith.science/paper/WCDRFYSO
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The paper

The paper claims

This review shows that evolving wormholes in cosmological backgrounds, especially in hybrid metric-Palatini gravity, can be supported by matter that obeys the null and weak energy conditions at all times.

The reading

This review collects and examines evolving wormhole solutions—wormholes whose geometry changes with time—embedded in expanding universes. In general relativity, static traversable wormholes need exotic matter that violates the null energy condition, but the paper shows that time dependence can localize or eliminate those violations. Its central constructive claim is that in hybrid metric-Palatini gravity, a modified theory that adds a scalar degree of freedom, there are traversable cosmological wormholes whose matter content satisfies the null and weak energy conditions at all times. If correct, this means wormholes could be embedded in a realistic cosmological history without requiring exotic matter.

What carries the argument

The central object is the conformally rescaled wormhole metric with a time-dependent conformal factor $\Omega(t)$ (or, in the hybrid gravity section, a scale factor $a(t)$) threaded by an anisotropic fluid with density, radial tension, and lateral pressure. The argument runs on two mechanisms: time dependence lets the WEC inequalities be satisfied for finite windows of cosmic time (Section 2), and the hybrid metric-Palatini scalar field, with its kinetic and potential terms entering the effective stress-energy tensor, supplies the extra degrees of freedom that remove the need for exotic matter. The load-bearing identity is the scalar-field equation of motion (Eq. 80), whose r-independence forces $b'(r)/r^2 = \mathrm{const}$ and hence the shape function $b(r) = r_0 + C H_0^2 (r^3 - r_0^3)/3$; setting $C=0$ reduces it to $b(r) = r_0$.

Extended reading notes

Core claim

The paper's central claim is that a wormhole metric of the form $ds^2 = -dt^2 + a^2(t)[dr^2/(1-b(r)/r) + r^2 d\Omega^2]$ can be an exact solution of hybrid metric-Palatini gravity with matter that never violates the null or weak energy conditions, provided the scalar field $\phi(t)$ is chosen to satisfy a specific differential equation. Concretely, taking the shape function $b(r) = r_0 + C H_0^2 (r^3 - r_0^3)/3$ with $C=0$ (so the throat geometry is the simplest allowed), a quartic scalar potential $U(\phi) = \phi^4$, and barotropic background equations of state $\omega_b = 1/3$ (radiation) or $\omega_b = 0$ (dust), the numerical solutions for $\phi(a)$ make $\rho$, $\rho-\tau$, and $\rho+p$ positive on the whole computed range $0.01 \le z \le 10^4$, for radial coordinates $r = r_0, 2r_0, 5r_0$. The energy conditions therefore hold 'at all times' in the reviewed solutions. The review also assembles earlier results showing that conformally related evolving wormholes in general relativity can satisfy the WEC for finite intervals, and that inflating wormholes violate the NEC near the throat.

Load-bearing premise

The conclusion that the energy conditions hold at all times rests on specific modeling choices—a time-dependent-only scalar field, the constant-throat shape function $b(r)=r_0$, a quartic potential, and fixed initial conditions—and on a numerical check over the finite redshift range $0.01 \le z \le 10^4$, so altering any of these choices could let the positivity fail.

Editorial extensions

If this is right

  • Traversable wormholes can be embedded in an expanding FLRW universe with ordinary matter, removing the main theoretical obstacle to their existence in cosmology.
  • In hybrid metric-Palatini gravity, the scalar field acts as an effective geometric source that allows the null and weak energy conditions to be satisfied at all times during radiation- and matter-dominated epochs.
  • In general relativity, evolving wormholes conformally related to static ones can obey the WEC for finite intervals of cosmic time, and particular scale factors can confine WEC violations to arbitrarily short 'flashes'.
  • Inflating wormholes in de Sitter backgrounds still violate the NEC near the throat, so the energy-condition-satisfying behaviour is specific to the hybrid gravity construction rather than generic to all evolving wormholes.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Beyond the paper's own claims, because the evidence for 'at all times' is numerical over $0.01 \le z \le 10^4$, a direct stress test would be to vary the potential or the initial conditions and check whether $\rho$, $\rho-\tau$, and $\rho+p$ stay positive throughout the range.
  • The same mechanism—imposing an $r$-independent scalar-field equation to fix the shape function—should extend to other modified gravity theories with extra scalar degrees of freedom, each giving different conditions on the throat geometry.
  • The review identifies dynamical stability as an open question; if these wormholes are unstable, the energy-condition-satisfying configurations would not persist, which would undercut their physical relevance.
Original 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-Lema\^itre-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.

The compiled record

The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 6,483 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.09 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.03 · compares with prior results 0.18 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

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-Lema\^itre-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.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 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. background 1.00 0.04 0.03 asserted 1.00
s1 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. background 0.99 0.04 0.04 asserted 1.00
s2 This review provides a comprehensive survey of evolving wormhole solutions, emphasizing their formulation within both general relativity and alternative theories of gravity. contribution 0.99 0.60 0.04 asserted 0.97
s3 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. contribution 0.97 0.61 0.03 asserted 0.94
s4 Particular attention is given to the wormholes embedded into Friedmann-Lema\^itre-Robertson-Walker (FLRW) universes and de Sitter backgrounds, where the interplay between the cosmic expansion and wormhole dynamics is analyzed. contribution 0.93 0.44 0.04 asserted 0.94
s5 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. contribution 0.80 0.22 0.18 asserted 0.94
s6 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. result 0.58 0.90 0.59 asserted 1.00
s7 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. interpretation 0.98 0.78 0.67 asserted 0.98

What kind of paper the classifier reports this is: review 1.00 · evidence from literature 0.99.

What was examined, and what was not

sources read
  • arXiv listing abstract v1
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
levels run
  • P abstract
not run
  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

Figures
Figure 1. A plot of F(t) vs. t for Ω(t) = sin(ω t) + a. Only the case of ω = 1 is considered, with respective values of (i) a = 1.5, (ii) a = 2, and (iii) a = 4. 2. Ω(t) = (t 2 + a 2 )/(t 2 + b 2 ), b > a > 0. This choice of the scale factor implies that asymptotically, the geometry becomes a static wormhole. The function F(t) is given by F(t) = 4(b 2 − a 2 )(3t 2 − a 2 ) (t 2 + b 2)(t 2 + a 2) 2 . (45) which is plotted in
Figure 2. A plot of F(t) vs. t for Ω(t) = (t 2 + a 2 )/(t 2 + b 2 ), b > a > 0, with a = 1. Cases of (i) b = 3, (ii) b = 2, and (iii) b = 1.5 are considered, respectively
Figure 3. The behaviors of ρ (which is independent of r according to Equation (81)), ρ − τ, and ρ + p, respectively, versus z for different values of r in the specific case of ωb = 1/3 with U(ϕ) = ϕ 4 . Note that both the horizontal and vertical axes are logarithmic. 0.01 0.10 1 10 100 1000 104 0.1 10 1000 105 107 109 1011 r0 2r0 5r0 0.01 0.10 1 10 100 1000 104 0.1 10 1000 105 107 109 1011 0.0 0.1 0.2 0.3 0.4 0.5 1.0 1.5 2.0 2.5 3.0 (a) ρ/3H2 0 vs z (b) (ρ − τ)/3H2 0 vs z r0 2r0 5r0 0.01 0.10 1 10 100 1000 104 0.1 10 1000 105 107 109 1011 0.0 0.1 0.2 0.3 0.4 1.0 1.5 2.0 2.5 3.0 (c) (ρ +…
Figure 4. The behaviors of ρ (which is independent of r according to Equation (81)), ρ − τ, and ρ + p, respectively, versus z for different values of r in the specific case of ωb = 0 with U(ϕ) = ϕ 4 . Both horizontal and vertical axes are logarithmic

Figures reproduced from arXiv:2507.14750 by the authors.

References
How the literature uses it

2 arXiv papers cite this in 2 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it

Cites it as background 2 papers

Discussion

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