Abstract
We consider a quantum scalar field in a classical (Euclidean) De Sitter background, whose radius is fixed dynamically by Einstein’s equations. In the case of a free scalar, it has been shown by Becker and Reuter that if one regulates the quantum effective action by putting a cutoff N on the modes of the quantum field, the radius is driven dynamically to infinity when N tends to infinity. We show that this result holds also in the case of a self-interacting scalar, both in the symmetric and broken-symmetry phase. Furthermore, when the gravitational background is put on shell, the quantum corrections to the mass and quartic self-coupling are found to be finite.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
S. Weinberg, The cosmological constant problem, Rev. Mod. Phys. 61 (1989) 1 [INSPIRE].
N. Straumann, CERN lectures on Einstein’s impact on the physics of the twentieth century, https://indico.cern.ch/event/425387/attachments/903020/1273882/lect.5.pdf, (2005).
Y.B. Zeldovich, Cosmological constant and elementary particles, JETP Lett. 6 (1967) 316 [INSPIRE].
E.K. Akhmedov, Vacuum energy and relativistic invariance, hep-th/0204048 [INSPIRE].
G. Ossola and A. Sirlin, Considerations concerning the contributions of fundamental particles to the vacuum energy density, Eur. Phys. J. C 31 (2003) 165 [hep-ph/0305050] [INSPIRE].
M. Maggiore, Zero-point quantum fluctuations and dark energy, Phys. Rev. D 83 (2011) 063514 [arXiv:1004.1782] [INSPIRE].
M. Asorey, P.M. Lavrov, B.J. Ribeiro and I.L. Shapiro, Vacuum stress-tensor in SSB theories, Phys. Rev. D 85 (2012) 104001 [arXiv:1202.4235] [INSPIRE].
B.S. DeWitt, Quantum field theory in curved space-time, Phys. Rept. 19 (1975) 295 [INSPIRE].
M. Becker and M. Reuter, Background independent field quantization with sequences of gravity-coupled approximants, Phys. Rev. D 102 (2020) 125001 [arXiv:2008.09430] [INSPIRE].
M. Becker and M. Reuter, Background independent field quantization with sequences of gravity-coupled approximants. II. Metric fluctuations, Phys. Rev. D 104 (2021) 125008 [arXiv:2109.09496] [INSPIRE].
R. Banerjee, M. Becker and R. Ferrero, N-cutoff regularization for fields on hyperbolic space, Phys. Rev. D 109 (2024) 025008 [arXiv:2302.03547] [INSPIRE].
E.J. Weinberg and A.-Q. Wu, Understanding complex perturbative effective potentials, Phys. Rev. D 36 (1987) 2474 [INSPIRE].
D. Benedetti, Critical behavior in spherical and hyperbolic spaces, J. Stat. Mech. 1501 (2015) P01002 [arXiv:1403.6712] [INSPIRE].
J. Madore, The fuzzy sphere, Class. Quant. Grav. 9 (1992) 69 [INSPIRE].
G. Fiore and F. Pisacane, Fuzzy circle and new fuzzy sphere through confining potentials and energy cutoffs, J. Geom. Phys. 132 (2018) 423 [arXiv:1709.04807] [INSPIRE].
C. Pagani and M. Reuter, Background independent quantum field theory and gravitating vacuum fluctuations, Annals Phys. 411 (2019) 167972 [arXiv:1906.02507] [INSPIRE].
R. Ferrero and M. Reuter, The spectral geometry of de Sitter space in asymptotic safety, JHEP 08 (2022) 040 [arXiv:2203.08003] [INSPIRE].
S.W. Hawking, Zeta function regularization of path integrals in curved space-time, Commun. Math. Phys. 55 (1977) 133 [INSPIRE].
R. Arnowitt, S. Deser and C.W. Misner, Finite self-energy of classical point particles, Phys. Rev. Lett. 4 (1960) 375 [INSPIRE].
B. DeWitt, Gravity: a universal regulator?, Phys. Rev. Lett. 13 (1964) 114 [INSPIRE].
C.J. Isham, A. Salam and J.A. Strathdee, Infinity suppression gravity modified quantum electrodynamics, Phys. Rev. D 3 (1971) 1805 [INSPIRE].
T. Thiemann, QSD 5: quantum gravity as the natural regulator of matter quantum field theories, Class. Quant. Grav. 15 (1998) 1281 [gr-qc/9705019] [INSPIRE].
S.L. Adler, Effective action model for the vanishing of the cosmological constant, Phys. Rev. Lett. 62 (1989) 373 [INSPIRE].
T.R. Taylor and G. Veneziano, Quenching the cosmological constant, Phys. Lett. B 228 (1989) 311 [INSPIRE].
T.R. Taylor and G. Veneziano, Quantum gravity at large distances and the cosmological constant, Nucl. Phys. B 345 (1990) 210 [INSPIRE].
Acknowledgments
We would like to thank D. Benedetti, V. Branchina, D. Ghilencea, S. Pögel and especially M. Reuter for useful discussions and comments.
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: 2404.12357
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
Ferrero, R., Percacci, R. The cosmological constant problem and the effective potential of a gravity-coupled scalar. J. High Energ. Phys. 2024, 74 (2024). https://doi.org/10.1007/JHEP09(2024)074
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP09(2024)074