Cosmic bounce and phantom-like equation of state from tunnelling
Open accessAbstract
We allow a scalar field on a flat FLRW background metric to tunnel between two degenerate vacua. The resulting true vacuum state then violates the Null Energy Condition, and the corresponding homogeneous fluid induces a bounce, after which it has a phantom-like equation of state and asymptotically leads to a de Sitter phase. The mechanism presented here requires no exotic matter or modified gravity, it is purely generated by quantum fluctuations and is valid for a generic double well potential.
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In Refs. [13, 21], the instanton contribution to the ground state energy is calculated by only keeping homogeneous fluctuations.
“In Refs. [13, 21], the instanton contribution to the ground state energy is calculated by only keeping homogeneous fluctuations.”
From Double-well instantons in finite volume (2024) · cites this paper as [21]
Section 2.2 says the calculation focuses on homogeneous saddle points, and Appendix B calculates fluctuation factors for the instanton contribution. But the paper does not say it keeps only homogeneous fluctuations: its discussion of quantum corrections describes using continuous momentum. The claim conflates a restriction on saddle points with a restriction on fluctuations. (LLM, conf=0.84)
Experimental — accuracy not yet measuredIncluding the Casimir energy and one-loop corrections to the instanton jump should not modify the qualitative results in Ref. [21] since the NEC is still violated for any value of the comoving volume.
“Including the Casimir energy and one-loop corrections to the instanton jump should not modify the qualitative results in Ref. [21] since the NEC is still violated for any value of the comoving volume, which means that we expect to find a bouncing solution to the Friedmann equations if we start from a contracting phase.”
From Double-well instantons in finite volume (2024) · cites this paper as [21]
Section 3.2 states that the ground-state fluid violates the NEC, and the Conclusions say that NEC violation produces a bounce after initial contraction. Appendix B includes fluctuations around instanton jumps. But the paper does not assess whether adding Casimir energy would leave those qualitative results unchanged; it mentions the Casimir effect only as a separate example of energy-condition violation. (LLM, conf=0.85)
Experimental — accuracy not yet measuredThe NEC is violated for any value of the comoving volume a3L03, and therefore a bouncing solution is obtained in FLRW independently of the initial conditions as long as H(t0) < 0.
“It can be shown (see Ref. [21]) that the NEC is violated for any value of the comoving volume a 3 L 3 0 , and therefore a bouncing solution is obtained in FLRW independently of the initial conditions as long as H ( t 0 ) < 0.”
From Double-well instantons in finite volume (2024) · cites this paper as [21]
Section 3.2, equation (3.11), states that the model’s ground-state fluid violates the NEC, and section 4 reports a bounce for a contracting FLRW solution. But section 4 studies numerical solutions with a fixed initial scale factor and varying parameter values; it does not establish a bounce independently of all initial conditions. Section 2.1 also assumes finite volume and adiabatic evolution, so the claim’s unqualified ‘any value’ is broader than the model’s stated scope. (LLM, conf=0.86)
Experimental — accuracy not yet measuredIn the simplified model analysed in Refs. [21, 22], where E_cas^(3)=0 and E_inst=E_inst^(hom), it was found L_bounce ≃ 10^-5 metres for U0=κ^-1Λ=10^-122 l_p^-4, m=10^-3 eV and λ∼1.
“For example, in the simplified model analysed in Refs. [21, 22], where E (3) cas = 0 and E inst = E (hom) inst with E (hom) inst given in Eq. (4.31), it was found L bounce ≃ 10 -5 metres for U 0 = κ -1 Λ = 10 -122 ℓ -4 p , m = 10 -3 eV and λ ∼ 1.”
From Double-well instantons in finite volume (2024) · cites this paper as [21]
Section 2.1 describes a finite-volume tunnelling model that focuses on tunnelling rather than the Casimir effect. The discussion around eqs. (5.1)–(5.2) estimates the bounce volume, but our copy does not report L_bounce ≃ 10⁻⁵ metres for the stated values of U₀, m and λ. Searches for the length and numerical values did not find that result. (LLM, conf=0.84)
Experimental — accuracy not yet measuredIn addition to the known Casimir effect, the tunnelling effect also contributes to NEC violation, extending the results in Ref. [21].
“In addition to the known Casimir effect, we show that the tunnelling effect also contributes to NEC violation, extending the results in Ref. [21].”
From Double-well instantons in finite volume (2024) · cites this paper as [21]
Ignoring the Casimir energy and the space-dependence of quantum fluctuations about the instanton, tunnelling can dynamically generate an effective equation of state that supports a cosmological bounce when coupled to gravity.
“Ignoring the Casimir energy and the space-dependence of quantum fluctuations about the instanton, it is found that tunnelling can indeed dynamically generate an effective equation of state that supports a cosmological bounce when coupled to gravity.”
From Double-well instantons in finite volume (2024) · cites this paper as [21]
The result of Refs. [13, 21] can be obtained from Eq. (4.29) by neglecting the contributions from n = 0 fluctuations.
“This can be obtained from the result in Eq. (4.29) by neglecting the contributions from n = 0 fl uctuations, namely”
From Double-well instantons in finite volume (2024) · cites this paper as [21]
Section 2.2, Eqs. (2.5)–(2.6), discusses fluctuation factors for saddle points, but does not say that neglecting n = 0 fluctuations recovers an earlier result. Searches for that condition and Eq. (4.29) found no matching statement in our copy. (LLM, conf=0.72)
Experimental — accuracy not yet measured
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Cites
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Cited by
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Double-well instantons in finite volume
Ai, W.-Y., Alexandre, J., Carosi, M., Garbrecht, B., & Pla, S. (2024) · Journal of High Energy Physics · doi:10.1007/jhep05(2024)099 · Cited by 6 · see citing works
Self-citation
- Authors
- Alexandre, J., & Pla, S.
- Affiliations
- King's College London (GB)
- Corresponding author
- Pla, Silvia
- Venue
- Journal of High Energy Physics
- Published
- 2023-05-17
- Volume
- 2023
- Issue
- 5
- ISSN
- 1029-8479 (ISSN-L)
- OpenAlex
- W4377107801
- Cited by
- 6
- References
- 4
- Citations by year
- 2025: 2 · 2024: 3 · 2023: 1
- FWCI
- 0.70
- Type
- journal article
- Language
- en
- Open access
- diamond
- doi.org
- Locations
- Journal of High Energy Physics (publishedVersion, cc-by)
- arXiv (Cornell University) (submittedVersion, cc-by)
- DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion, cc-by-sa)
- Research Portal (King's College London) (submittedVersion, other-oa)
- arXiv (Cornell University) (cc-by)
- Funders
- Leverhulme Trust (RPG-2021-299)
- Engineering and Physical Sciences Research Council (EP/V002821/1)
- Science and Technology Facilities Council (ST/T000759/1, STFC-ST/T000759/1)
- Topics
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Cosmology and Gravitation Theories
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Noncommutative and Quantum Gravity Theories
- Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Black Holes and Theoretical Physics
- Keywords
- bounce cosmology, phantom equation of state, tunneling, scalar field, degenerate vacua, null energy condition violation, de Sitter phase, double-well potential, quantum fluctuations, FLRW metric, true vacuum
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