Abstract
I try to revive, and possibly reconcile, a debate started a few years ago, about the relative roles of a bare cosmological constant and of a vacuum energy, by taking the attitude to try to get the most from the physics now available as established. I notice that the bare cosmological constant of the Einstein equations, which is there ever since GR emerged, is actually constrained (if not measured) indirectly combining the effective cosmological constant observed now, as given by ΛCDM Precision Cosmology, with the cumulative vacuum contribution of the particles of the Standard Model, SM. This comes out when the vacuum energy is regularized, as given by many Authors, still within well established Quantum Field Theory, QFT, but without violating Lorentz invariance. The fine tuning, implied by the compensation to a small positive value of the two large contributions, could be seen as offered by Nature, which provides one more fundamental constant, the bare Lambda. The possibility is then discussed of constraining (measuring) directly such a bare cosmological constant by the features of primordial gravitational wave signals coming from epoch’s precedent to the creation of particles. I comment on possibilities that would be lethal, that is if the vacuum does not gravitate. This last issue is often raised, and I discuss the current situation about. Finally a hint is briefly discussed for a possible “bare Lambda inflation” process.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Bianchi, E., Rovelli, C.: Why all these prejudices against a constant?. arXiv:1002.3966v3[astro-ph.CO] 11 April 2010
Dadhich, N.: On the enigmatic Λ—a true constan of spacetime. arXiv:1006.1552v2 21 Feb 2011; see also of the same Author arXiv:1105.3396 and arXiv:1609.02138
Bianchi, E., Rovelli, C., Kolb, R.: Cosmology forum: is dark energy really a mystery? Nature 466, 321–322 (2010)
Koksma, J.F., Prokopec, T.: The cosmological constant and lorentz invariance of the vacuum state. arXiv:1105.6296v1 [gr-qc] 31 May 2011
by now I mean the cosmic time when the creation of all the SM particles had been completed and the contribution of a Λeff to the expansion of the Universe is found constant within the precision of current observations
“well understood and experimentally tested laws…” from Table I in TASI Lectures on inflation by Baumann D.: arXiv:0907.5424v2 (2012); I am using the term well established physics to summarize what has been remarked therein about the history of the Universe “…from 10−10 seconds [corresponding to the electroweak unification at an energy of 1 TeV] to today the history of the universe is based on well understood and experimentally tested laws of particle physics, nuclear and atomic physics and gravity”
however Lorentz violating theories as Horava gravity are amenable to renormalization and still compatible with observations, see for instance Wang, A.: Hořava gravity at a Lifshitz point: a progress report. Int. J. Mod. Phys. D 26, 1730014 (2017); I thank S. Liberati for pointing this to me
Akhmedov, E.K.: Vacuum energy and relativistic invariance. arXiv:hep-th/0204048v2 (2002)
Martin, J.: Everything you always wanted to know about the cosmological constant problem (but were afraid to ask) in understanding the dark universe Comptes Rendues Physique 13(6-7), 566–665 (2012)
Ashtekar, A.: Implications of a positive cosmological constant for general relativity. Rep. Prog. Phys. 80, 102901 (2017)
Caprini, C., Figueroa, D.G.: Cosmological backgrounds of gravitational waves. arXiv:1801.04268 [astro-ph.CO] 5 Feb 2018
Näf, J., Jetzer, P., Sereno, M.: On gravitational waves in spacetimes with a nonvanishing cosmological constant. Phys. Rev. D 79, 024014 (2009)
Visser, M.: Lorentz invariance and the zero-point stress-energy tensor. Particles 1, 138 (2018)
Lombriser, L.: On the cosmological constant problem. arXiv:1901.08588v1 [gr-qc] 23 Jan 2019
Nikolić, H.: Proof that Casimir force does not originate from vacuum energy. Phys. Lett. B 761, 197 (2016)
Cerdonio M., Rovelli C.: Casimir effects are not an experimental demonstration that free vacuum gravitates: connections to the cosmological constant problem, J Mod Phys D 24, 1544020 (2015) [special issue publishing a selection of Essays awarded with Honorable Mention by the Gravity Research Foundation 2015 Awards]; Cerdonio M. and Rovelli C.: Casimir cavities do not fly. arXiv:1406.1105v3
Mostepanenko, V.M., Klimchitskaya, G.L.: Whether an enormously large energy density of the quantum vacuum is catastrophic. arXiv:1903.04261v1 [physics.gen-ph] 2 March 2019
Jaffe, R.L.: Casimir effect and the quantum vacuum. Phys. Rev. D 72, 021301 (2005)
Herrera, R., Pavon, D., Saavedra, J.: Constraints on the radiation temperature before inflation. arXiv:1801.06155v1 [gr-qc] 18 Jan 2018
Planck 2015 results: A&A 594, A13 (2016)
Acknowledgements
I am grateful to my wife Annamaria for bearing with me during the preparation of this paper and to Naresh Dadhich for correspondence on the matter. I thank Alessandro Bettini and Gianni Carugno for lively discussions. I am thankful to Philippe Jetzer for a discussion and for helpful suggestions. I am much indebted to Stefano Liberati for a critical reading of the manuscript, with comments I took in due consideration for the present version.
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.
Rights and permissions
About this article
Cite this article
Cerdonio, M. About the Measure of the Bare Cosmological Constant. Found Phys 49, 830–836 (2019). https://doi.org/10.1007/s10701-019-00285-9
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10701-019-00285-9