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Solà Peracaula J. The cosmological constant problem and running vacuum in the expanding universe. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2022; 380:20210182. [PMID: 35785977 DOI: 10.1098/rsta.2021.0182] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/13/2021] [Accepted: 03/17/2022] [Indexed: 06/15/2023]
Abstract
It is well known that quantum field theory (QFT) induces a huge value of the cosmological constant (CC), [Formula: see text], which is outrageously inconsistent with cosmological observations. We review here some aspects of this fundamental theoretical conundrum (the cosmological constant problem, CCP) and strongly argue in favour of the possibility that the cosmic vacuum density [Formula: see text] may be mildly evolving with the expansion rate [Formula: see text]. Such a 'running vacuum model' (RVM) proposal predicts an effective dynamical dark energy without postulating new ad hoc fields (quintessence and the like). Using the method of adiabatic renormalization within QFT in curved space-time, we find that [Formula: see text] acquires a dynamical component [Formula: see text] caused by the quantum matter effects. There are also [Formula: see text] ([Formula: see text]) contributions, some of which may trigger inflation in the early universe. Remarkably, the evolution of the adiabatically renormalized [Formula: see text] is not affected by dangerous terms proportional to the quartic power of the masses ([Formula: see text]) of the quantized matter fields. Traditionally, these terms have been the main source of trouble as they are responsible for the extreme fine-tuning feature of the CCP. In the context under study, however, the late time [Formula: see text] around [Formula: see text] is given by a dominant term ([Formula: see text]) plus the aforementioned mild dynamical component [Formula: see text] (with [Formula: see text]), which makes the RVM to mimic quintessence. Finally, on the phenomenological side, we show that the RVM may be instrumental in alleviating some of the most challenging problems (so-called 'tensions') afflicting nowadays the observational consistency of the 'concordance' [Formula: see text]CDM model, such as the [Formula: see text] and [Formula: see text] tensions. This article is part of the theme issue 'The future of mathematical cosmology, Volume 2'.
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Affiliation(s)
- Joan Solà Peracaula
- Departament de Física Quàntica i Astrofísica, and Institute of Cosmos Sciences, Universitat de Barcelona, Av. Diagonal 647, E-08028 Barcelona, Catalonia, Spain
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Abstract
By analyzing the energy-momentum tensor and equations of state of ideal gas, scalar, spinor and vector potential in detail, we find that the total mass density of all matter is always positive, and the initial total pressure is negative. Under these conditions, by qualitatively analyzing the global behavior of the dynamical equation of cosmological model, we get the following results: (i) K=1, namely, the global spatial structure of the universe should be a three-dimensional sphere S3; (ii) 0≤Λ<10−24ly−2, the cosmological constant should be zero or an infinitesimal; (iii) a(t)>0, the initial singularity of the universe is unreachable, and the evolution of the universe should be cyclic in time. Since the matter components considered are quite complete and the proof is very elementary and strict, these conclusions are quite reliable in logic and compatible with all observational data. Obviously, these conclusions will be very helpful to correct some popular misconceptions and bring great convenience to further research other problems in cosmology such as the properties of dark matter and dark energy. In addition, the macroscopic Lagrangian of fluid model is derived.
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Abstract
We study the homogeneous but anisotropic Bianchi type-V cosmological model with time-dependent gravitational and cosmological “constants”. Exact solutions of the Einstein field equations (EFEs) are presented in terms of adjustable parameters of quantum field theory in a spatially curved and expanding background. It has been found that the general solution of the average scale factor a as a function of time involved the hypergeometric function. Two cosmological models are obtained from the general solution of the hypergeometric function and the Emden–Fowler equation. The analysis of the models shows that, for a particular choice of parameters in our first model, the cosmological “constant” decreases whereas the Newtonian gravitational “constant” increases with time, and for another choice of parameters, the opposite behaviour is observed. The models become isotropic at late times for all parameter choices of the first model. In the second model of the general solution, both the cosmological and gravitational “constants” decrease while the model becomes more anisotropic over time. The exact dynamical and kinematical quantities have been calculated analytically for each model.
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Paliathanasis A, Tsamparlis M, Basilakos S, Capozziello S. Scalar-tensor gravity cosmology: Noether symmetries and analytical solutions. Int J Clin Exp Med 2014. [DOI: 10.1103/physrevd.89.063532] [Citation(s) in RCA: 35] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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Das K, Ali N. Axially Symmetric Bianchi Type-I Bulk Viscous Cosmological Model with Time Varying Gravitational and Cosmological Constants. NATIONAL ACADEMY SCIENCE LETTERS 2014. [DOI: 10.1007/s40009-013-0222-3] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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Linearly Varying Deceleration Parameter in Viscous Bianchi Type I Universe. PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES INDIA SECTION A-PHYSICAL SCIENCES 2013. [DOI: 10.1007/s40010-012-0054-4] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/26/2022]
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Bernard D, LeClair A. Scrutinizing the cosmological constant problem and a possible resolution. Int J Clin Exp Med 2013. [DOI: 10.1103/physrevd.87.063010] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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Bianchi Type III Dust Filled Universe with Time Dependent Λ in C-Field Cosmology. PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES INDIA SECTION A-PHYSICAL SCIENCES 2013. [DOI: 10.1007/s40010-012-0055-3] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
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Costa FEM, Alcaniz JS. Cosmological consequences of a possibleΛ-dark matter interaction. Int J Clin Exp Med 2010. [DOI: 10.1103/physrevd.81.043506] [Citation(s) in RCA: 39] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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Debnath PS, Paul BC, Beesham A. Viscous cosmologies with variableΛin higher derivative gravity. Int J Clin Exp Med 2007. [DOI: 10.1103/physrevd.76.123505] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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Dodelson S, Kaplinghat M, Stewart E. Solving the coincidence problem: tracking oscillating energy. PHYSICAL REVIEW LETTERS 2000; 85:5276-5279. [PMID: 11135975 DOI: 10.1103/physrevlett.85.5276] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/24/2000] [Revised: 06/26/2000] [Indexed: 05/23/2023]
Abstract
Recent cosmological observations strongly suggest that the Universe is dominated by an unknown form of energy with negative pressure. Why is this dark energy density of order the critical density today? We propose that the dark energy has periodically dominated in the past so that its preponderance today is natural. We illustrate this paradigm with a model potential and show that its predictions are consistent with all observations.
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Affiliation(s)
- S Dodelson
- NASA/Fermilab Astrophysics Center, Fermi National Accelerator Laboratory, Batavia, Illinois 60510-0500, USA
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Lima JA. Thermodynamics of decaying vacuum cosmologies. PHYSICAL REVIEW. D, PARTICLES AND FIELDS 1996; 54:2571-2577. [PMID: 10020937 DOI: 10.1103/physrevd.54.2571] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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Lima JA, Trodden M. Decaying vacuum energy and deflationary cosmology in open and closed universes. PHYSICAL REVIEW. D, PARTICLES AND FIELDS 1996; 53:4280-4286. [PMID: 10020425 DOI: 10.1103/physrevd.53.4280] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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Lima JA, Maia A. Thermodynamic properties of gamma fluids and the quantum vacuum. PHYSICAL REVIEW. D, PARTICLES AND FIELDS 1995; 52:5628-5635. [PMID: 10019092 DOI: 10.1103/physrevd.52.5628] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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Matyjasek J. Cosmological models with a time-dependent Lambda term. PHYSICAL REVIEW. D, PARTICLES AND FIELDS 1995; 51:4154-4159. [PMID: 10018890 DOI: 10.1103/physrevd.51.4154] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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Arbab AI, Abdel-Rahman AM. Nonsingular cosmology with a time-dependent cosmological term. PHYSICAL REVIEW. D, PARTICLES AND FIELDS 1994; 50:7725-7728. [PMID: 10017755 DOI: 10.1103/physrevd.50.7725] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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Maia MD, Silva GS. Geometrical constraints on the cosmological constant. PHYSICAL REVIEW. D, PARTICLES AND FIELDS 1994; 50:7233-7238. [PMID: 10017704 DOI: 10.1103/physrevd.50.7233] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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Silveira V, Waga I. Decaying Lambda cosmologies and power spectrum. PHYSICAL REVIEW. D, PARTICLES AND FIELDS 1994; 50:4890-4894. [PMID: 10018141 DOI: 10.1103/physrevd.50.4890] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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Arcuri RC, Waga I. Growth of density inhomogeneities in Newtonian cosmological models with variable Lambda. PHYSICAL REVIEW. D, PARTICLES AND FIELDS 1994; 50:2928-2931. [PMID: 10017925 DOI: 10.1103/physrevd.50.2928] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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Lima JA, Maia JM. Deflationary cosmology with decaying vacuum energy density. PHYSICAL REVIEW. D, PARTICLES AND FIELDS 1994; 49:5597-5600. [PMID: 10016879 DOI: 10.1103/physrevd.49.5597] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Beesham A. Cosmological models with a variable cosmological term and bulk viscous models. PHYSICAL REVIEW. D, PARTICLES AND FIELDS 1993; 48:3539-3543. [PMID: 10016625 DOI: 10.1103/physrevd.48.3539] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Abdalla TM, Abdel-Rahman AM. Singularity-free decaying-vacuum cosmologies: Evolution of density perturbations. Int J Clin Exp Med 1992; 46:5675-5677. [PMID: 10014956 DOI: 10.1103/physrevd.46.5675] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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Carvalho JC, Lima JA, Waga I. Cosmological consequences of a time-dependent Lambda term. PHYSICAL REVIEW. D, PARTICLES AND FIELDS 1992; 46:2404-2407. [PMID: 10015170 DOI: 10.1103/physrevd.46.2404] [Citation(s) in RCA: 15] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Abdel-Rahman AM. Singularity-free decaying-vacuum cosmologies. PHYSICAL REVIEW. D, PARTICLES AND FIELDS 1992; 45:3497-3511. [PMID: 10014244 DOI: 10.1103/physrevd.45.3497] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Calvao MO, Pavón D, Salim JM. Dissipative cosmology with decaying vacuum energy. PHYSICAL REVIEW. D, PARTICLES AND FIELDS 1992; 45:3869-3872. [PMID: 10014281 DOI: 10.1103/physrevd.45.3869] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Berman MS. Cosmological models with a variable cosmological term. PHYSICAL REVIEW. D, PARTICLES AND FIELDS 1991; 43:1075-1078. [PMID: 10013478 DOI: 10.1103/physrevd.43.1075] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Pavón D. Nonequilibrium fluctuations in cosmic vacuum decay. PHYSICAL REVIEW. D, PARTICLES AND FIELDS 1991; 43:375-378. [PMID: 10013397 DOI: 10.1103/physrevd.43.375] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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