Abstract
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.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
K. Symanzik, Renormalizable models with simple symmetry breaking. 1. Symmetry breaking by a source term, Commun. Math. Phys. 16 (1970) 48 [INSPIRE].
S.R. Coleman, R. Jackiw and H.D. Politzer, Spontaneous Symmetry Breaking in the O(N) Model for Large N, Phys. Rev. D 10 (1974) 2491 [INSPIRE].
J. Iliopoulos, C. Itzykson and A. Martin, Functional Methods and Perturbation Theory, Rev. Mod. Phys. 47 (1975) 165 [INSPIRE].
R.W. Haymaker and J. Perez-Mercader, Convexity of the Effective Potential, Phys. Rev. D 27 (1983) 1948 [INSPIRE].
Y. Fujimoto, L. O’Raifeartaigh and G. Parravicini, Effective Potential for Nonconvex Potentials, Nucl. Phys. B 212 (1983) 268 [INSPIRE].
C.M. Bender and F. Cooper, Failure of the Naive Loop Expansion for the Effective Potential in ϕ4 Field Theory When There Is ‘Broken Symmetry’, Nucl. Phys. B 224 (1983) 403 [INSPIRE].
M. Hindmarsh and D. Johnston, Convexity of the Effective Potential, J. Phys. A 19 (1986) 141 [INSPIRE].
A.D. Plascencia and C. Tamarit, Convexity, gauge-dependence and tunneling rates, JHEP 10 (2016) 099 [arXiv:1510.07613] [INSPIRE].
P. Millington and P.M. Saffin, Visualising quantum effective action calculations in zero dimensions, J. Phys. A 52 (2019) 405401 [arXiv:1905.09674] [INSPIRE].
J. Alexandre and A. Tsapalis, Maxwell Construction for Scalar Field Theories with Spontaneous Symmetry Breaking, Phys. Rev. D 87 (2013) 025028 [arXiv:1211.0921] [INSPIRE].
J. Alexandre and D. Backhouse, One-loop tunneling-induced energetics, Phys. Rev. D 105 (2022) 105018 [arXiv:2203.12543] [INSPIRE].
J. Alexandre and J. Polonyi, Symmetry restoration, tunneling, and the null energy condition, Phys. Rev. D 106 (2022) 065008 [arXiv:2205.00768] [INSPIRE].
J. Alexandre and D. Backhouse, NEC violation: Tunnelling versus the Casimir effect, arXiv:2301.02455 [INSPIRE].
V.A. Rubakov, The Null Energy Condition and its violation, Phys. Usp. 57 (2014) 128 [arXiv:1401.4024] [INSPIRE].
E.-A. Kontou and K. Sanders, Energy conditions in general relativity and quantum field theory, Class. Quant. Grav. 37 (2020) 193001 [arXiv:2003.01815] [INSPIRE].
T.W.B. Kibble, Topology of Cosmic Domains and Strings, J. Phys. A 9 (1976) 1387 [INSPIRE].
W.H. Zurek, Cosmological Experiments in Superfluid Helium?, Nature 317 (1985) 505 [INSPIRE].
H.B.G. Casimir, On the Attraction Between Two Perfectly Conducting Plates, Indag. Math. 10 (1948) 261 [INSPIRE].
P.C.W. Davies and S.A. Fulling, Radiation from Moving Mirrors and from Black Holes, Proc. Roy. Soc. Lond. A 356 (1977) 237 [INSPIRE].
S.W. Hawking, Particle Creation by Black Holes, Commun. Math. Phys. 43 (1975) 199 [Erratum ibid. 46 (1976) 206] [INSPIRE].
V.K. Onemli and R.P. Woodard, Superacceleration from massless, minimally coupled φ4, Class. Quant. Grav. 19 (2002) 4607 [gr-qc/0204065] [INSPIRE].
E.-A. Kontou and K.D. Olum, Energy conditions allow eternal inflation, JCAP 03 (2021) 097 [arXiv:2008.01878] [INSPIRE].
S.R. Coleman, The Fate of the False Vacuum. 1. Semiclassical Theory, Phys. Rev. D 15 (1977) 2929 [Erratum ibid. 16 (1977) 1248] [INSPIRE].
C.G. Callan Jr. and S.R. Coleman, The Fate of the False Vacuum. 2. First Quantum Corrections, Phys. Rev. D 16 (1977) 1762 [INSPIRE].
A. Andreassen, D. Farhi, W. Frost and M.D. Schwartz, Precision decay rate calculations in quantum field theory, Phys. Rev. D 95 (2017) 085011 [arXiv:1604.06090] [INSPIRE].
W.-Y. Ai, B. Garbrecht and C. Tamarit, Functional methods for false vacuum decay in real time, JHEP 12 (2019) 095 [arXiv:1905.04236] [INSPIRE].
H. Kleinert, Path Integrals in Quantum Mechanics, Statistics, Polymer Physics, and Financial Markets [INSPIRE].
K.J. Ludwick, The viability of phantom dark energy: A review, Mod. Phys. Lett. A 32 (2017) 1730025 [arXiv:1708.06981] [INSPIRE].
P.J. Steinhardt and N. Turok, Cosmic evolution in a cyclic universe, Phys. Rev. D 65 (2002) 126003 [hep-th/0111098] [INSPIRE].
J. Khoury, B.A. Ovrut, P.J. Steinhardt and N. Turok, The Ekpyrotic universe: Colliding branes and the origin of the hot big bang, Phys. Rev. D 64 (2001) 123522 [hep-th/0103239] [INSPIRE].
J. Khoury et al., From big crunch to big bang, Phys. Rev. D 65 (2002) 086007 [hep-th/0108187] [INSPIRE].
A.H. Guth, The Inflationary Universe: A Possible Solution to the Horizon and Flatness Problems, Phys. Rev. D 23 (1981) 347 [INSPIRE].
A.D. Linde, A New Inflationary Universe Scenario: A Possible Solution of the Horizon, Flatness, Homogeneity, Isotropy and Primordial Monopole Problems, Phys. Lett. B 108 (1982) 389 [INSPIRE].
J. Alexandre and K. Clough, Saving the universe with finite volume effects, Phys. Rev. D 100 (2019) 103522 [arXiv:1906.10662] [INSPIRE].
J. Alexandre and J. Polonyi, Tunnelling and dynamical violation of the Null Energy Condition, Phys. Rev. D 103 (2021) 105020 [arXiv:2101.08640] [INSPIRE].
M. Bordag, U. Mohideen and V.M. Mostepanenko, New developments in the Casimir effect, Phys. Rept. 353 (2001) 1 [quant-ph/0106045] [INSPIRE].
L.E. Parker and D. Toms, Quantum Field Theory in Curved Spacetime: Quantized Field and Gravity, Cambridge Monographs on Mathematical Physics, Cambridge University Press (2009) [https://doi.org/10.1017/CBO9780511813924] [INSPIRE].
B.L. Hu and D.J. O’Connor, Effective Lagrangian for λϕ4 Theory in Curved Space-time With Varying Background Fields: Quasilocal Approximation, Phys. Rev. D 30 (1984) 743 [INSPIRE].
T. Markkanen, S. Nurmi, A. Rajantie and S. Stopyra, The 1-loop effective potential for the Standard Model in curved spacetime, JHEP 06 (2018) 040 [arXiv:1804.02020] [INSPIRE].
D.V. Vassilevich, Heat kernel expansion: User’s manual, Phys. Rept. 388 (2003) 279 [hep-th/0306138] [INSPIRE].
J.S. Schwinger, On gauge invariance and vacuum polarization, Phys. Rev. 82 (1951) 664 [INSPIRE].
P.B. Gilkey, The Spectral geometry of a Riemannian manifold, J. Diff. Geom. 10 (1975) 601 [INSPIRE].
L. Parker and D.J. Toms, New Form for the Coincidence Limit of the Feynman Propagator, or Heat Kernel, in Curved Space-time, Phys. Rev. D 31 (1985) 953 [INSPIRE].
I. Jack and L. Parker, Proof of Summed Form of Proper Time Expansion for Propagator in Curved Space-time, Phys. Rev. D 31 (1985) 2439 [INSPIRE].
B.-L.B. Hu and E. Verdaguer, Semiclassical and Stochastic Gravity: Quantum Field Effects on Curved Spacetime, Cambridge Monographs on Mathematical Physics, Cambridge University Press (2020) [https://doi.org/10.1017/9780511667497] [INSPIRE].
T. Markkanen and A. Tranberg, A Simple Method for One-Loop Renormalization in Curved Space-Time, JCAP 08 (2013) 045 [arXiv:1303.0180] [INSPIRE].
G.V. Dunne, Functional determinants in quantum field theory, in the proceedings of the 14th WE Heraeus Saalburg summer school Wolfersdorf, Thuringia (2009) [https://saalburg.aei.mpg.de/wp-content/uploads/sites/25/2017/03/dunne.pdf].
Acknowledgments
The authors thank Katy Clough and Malcolm Fairbairn for cosmology-related discussions, as well as Jose Navarro-Salas and Janos Polonyi for insightful comments. This work is supported by the Leverhulme Trust (grant RPG-2021-299) and the Science and Technology Facilities Council (grant STFC-ST/T000759/1).
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 2301.08652
Rights and permissions
Open Access . This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
About this article
Cite this article
Alexandre, J., Pla, S. Cosmic bounce and phantom-like equation of state from tunnelling. J. High Energ. Phys. 2023, 145 (2023). https://doi.org/10.1007/JHEP05(2023)145
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP05(2023)145