JHEPGC  Vol.5 No.1 , January 2019
Is Quintessence an Indication of a Time-Varying Gravitational Constant?
ABSTRACT
A model is presented where the quintessence parameter, w, is related to a time-varying gravitational constant. Assuming a present value of w = -0.98 , we predict a current variation of Ġ/G = -0.06H0, a value within current observational bounds. H0 is Hubble’s parameter, G is Newton’s constant and Ġ is the derivative of G with respect to time. Thus, G has a cosmic origin, is decreasing with respect to cosmological time, and is proportional to H0, as originally proposed by the Dirac-Jordan hypothesis, albeit at a much slower rate. Within our model, we can explain the cosmological constant fine-tuning problem, the discrepancy between the present very weak value of the cosmological constant, and the much greater vacuum energy found in earlier epochs (we assume a connection exists). To formalize and solidify our model, we give two distinct parametrizations of G with respect to “a”, the cosmic scale parameter. We treat G-1 as an order parameter, which vanishes at high energies; at low temperatures, it reaches a saturation value, a value we are close to today. Our first parametrization for G-1 is motivated by a charging capacitor; the second treats G-1(a) by analogy to a magnetic response, i.e., as a Langevin function. Both parametrizations, even though very distinct, give a remarkably similar tracking behavior for w(a) , but not of the conventional form, w(a) = w0 + wa(1-a) , which can be thought of as only holding over a limited range in “a”. Interestingly, both parametrizations indicate the onset of G formation at a temperature of approximately 7×1021 degrees Kelvin, in contrast to the ΛCDM model where G is taken as a constant all the way back to the Planck temperature, 1.42×1032 degrees Kelvin. At the temperature of formation, we find that G has increased to roughly 4×1020 times its current value. For most of cosmic evolution, however, our variable G model gives results similar to the predictions of the ΛCDM model, except in the very early universe, as we shall demonstrate. In fact, in the limit where w approaches -1, the expression, Ġ/G , vanishes, and we are left with the concordance model. Within our framework, the emergence of dark energy over matter at a scale of a ≈ 0.5 is that point where G-1 increases noticeably to its current value, G0-1 . This weakening of G to its current value G0 is speculated as the true cause for the observed unanticipated acceleration of the universe.
Cite this paper
Pilot, C. (2019) Is Quintessence an Indication of a Time-Varying Gravitational Constant?. Journal of High Energy Physics, Gravitation and Cosmology, 5, 41-81. doi: 10.4236/jhepgc.2019.51003.
References
[1]   Weinberg, S. (1989) The Cosmological Constant Problem. Reviews of Modern Physics, 61, 1.
https://doi.org/10.1103/RevModPhys.61.1

[2]   Copeland, E.J., Sami, M. and Tsujikawa, S. (2006) Dynamics of Dark Energy. International Journal of Modern Physics D, 15, 1753.

[3]   Tsujikawa, S. (2010) Modified Gravity Models of Dark Energy. Lecture Notes in Physics, 800, 99.

[4]   Fujii, Y. (1982) Origin of the Gravitational Constant and Particle Masses in a Scale-Invariant Scalar-Tensor Theory. Physical Review D, 26, 2580.
https://doi.org/10.1103/PhysRevD.26.2580

[5]   Ford, L.H. (1987) Cosmological-Constant Damping by Unstable Scalar Fields. Physical Review D, 35, 2339.
https://doi.org/10.1103/PhysRevD.35.2339

[6]   Wetterich, C. (1988) Cosmology and the Fate of Dilatation Symmetry. Nuclear Physics B, 302, 668-696.
https://doi.org/10.1016/0550-3213(88)90193-9

[7]   Chiba, T., Sugiyama, N. and Nakamura, T. (1997) Cosmology with x-Matter. Monthly Notices of the Royal Astronomical Society, 289, L5-L9.
https://doi.org/10.1093/mnras/289.2.L5

[8]   Ferreira, P.G. and Joyce, M. (1997) Structure Formation with a Self-Tuning Scalar Field. Physical Review Letters, 79, 4740.
https://doi.org/10.1103/PhysRevLett.79.4740

[9]   Caldwell, R.R., Dave, R. and Steinhardt, P.J. (1998) Cosmological Imprint of an Energy Component with General Equation of State. Physical Review Letters, 80, 1582.
https://doi.org/10.1103/PhysRevLett.80.1582

[10]   Peebles, P.J.E. and Ratra, B. (1988) Cosmology with a Time-Variable Cosmological “Constant”. Astrophysical Journal, 325, L17-L20.
https://doi.org/10.1086/185100

[11]   Ratra, B. and Peebles, J. (1988) Cosmological Consequences of a Rolling Homogeneous Scalar Field. Physical Review D, 37, 3406.
https://doi.org/10.1103/PhysRevD.37.3406

[12]   Komatsu, E., et al. (2011) WMAP Collaboration. The Astrophysical Journal Supplement, 192, 18.

[13]   Lahav, O. and Liddle, A.R. (2015) Cosmological Parameters. The Value Quoted Here Is , Based on a Compilation of CMB, SN and BAO Measurements Assuming a Flat Universe.

[14]   Ade, P.A.R., Aghanim, N., Armitage-Caplan, C., Arnaud, M., et al. (2015) Planck 2015 Results. XIII. Cosmological Parameters.
https://arXiv.org/abs/1502.1589v2

[15]   (2016) Planck Collaboration XIV, Planck 2015 Results. XIV. Dark Energy and Modified Gravity. A&A, in Press, arXiv: 1502.01590.

[16]   Dirac, P.A.M. (1937) The Cosmological Constants. Nature, 139, 323.
https://doi.org/10.1038/139323a0

[17]   Dirac, P.A.M. (1938) A New Basis for Cosmology. Proceedings of the Royal Society of London A, 165, 199-208.
https://doi.org/10.1098/rspa.1938.0053

[18]   Dirac, P.A.M. (1974) Cosmological Models and the Large Numbers Hypothesis. Proceedings of the Royal Society of London A, 338, 439-446.
https://doi.org/10.1098/rspa.1974.0095

[19]   Jordan, P. (1937) G Has to Be a Field. Naturwiss, 25, 513-517.
https://doi.org/10.1007/BF01498368

[20]   Jordan, P. (1949) Formation of Stars and Development of the Universe. Nature, 164, 637-640.
https://doi.org/10.1038/164637a0

[21]   Vieweg, F. and Sohn, B. (1966) Heinz Haber: “Die Expansion der Erde” [The Expansion of the Earth] Unser blauer Planet [Our Blue Planet]. Rororo Sachbuch [Rororo Nonfiction] (in German) (Rororo Taschenbuch Ausgabe [Rororo Pocket Edition] ed.). Rowohlt Verlag, Reinbek, 48, 52, 54-55.

[22]   Kragh, H. (2015) Pascual Jordan, Varying Gravity, and the Expanding Earth. Physics in Perspective, 17, 107-134.
http://adsabs.harvard.edu/abs/2015PhP...17..107K
https://doi.org/10.1007/s00016-015-0157-9


[23]   Muller, P.M. (1978) On the Measurement of Cosmological Variations of the Gravitational Constant. In: Halphern, L., Ed., University of Florida, Gainesville, 93.

[24]   Shapiro, I.I., Smith, W.B. and Ash, M.B. (1971) Gravitational Constant: Experimental Bound on Its Time Variation. Physical Review Letters, 26, 27.
https://doi.org/10.1103/PhysRevLett.26.27

[25]   Van Flandern, T.C. (1971) Lunar Ephemeris and Astrometric Corrections from Occultations. Astrophysical Journal, 76, 81.
https://doi.org/10.1086/111088

[26]   Van Flandern, T.C. (1975) A Determination of the Rate of Change of G. Monthly Notices of the Royal Astronomical Society, 170, 333-342.
https://doi.org/10.1093/mnras/170.2.333

[27]   Martins, J.A.P. (2002) Cosmology with Varying Constants. Philosophical Transactions of the Royal Society A, 360, 2681-2695.

[28]   Uzan, J.P. (2003) The Fundamental Constants and Their Variation, Observational Status and Theoretical Motivations. Reviews of Modern Physics, 75, 403.
http://adsabs.harvard.edu/abs/2003RvMP...75..403U
https://doi.org/10.1103/RevModPhys.75.403


[29]   Barrow, J.D. (2005) Varying Constants. Philosophical Transactions of the Royal Society A, 363, 2139-2153.

[30]   Uzan, J.P. (2011) Varying Constants, Gravitation and Cosmology. Living Reviews in Relativity, 14, 2.
https://doi.org/10.12942/lrr-2011-2

[31]   Nordtvedt, K. (1968) Testing Relativity with Laser Ranging to the Moon. Physical Review, 170, 1186.
https://doi.org/10.1103/PhysRev.170.1186

[32]   Nordtvedt, K. (1988) Lunar Laser Ranging and Laboratory Eötvös-Type Experiments. Physical Review D, 37, 1070.
https://doi.org/10.1103/PhysRevD.37.1070

[33]   Nordtvedt, K. (1990) Ġ/G and a Cosmological Acceleration of Gravitationally Compact Bodies. Physical Review Letters, 65, 953.
https://doi.org/10.1103/PhysRevLett.65.953

[34]   Thorsett, S.E. (1996) The Gravitational Constant, The Chandrasekhar Limit, and Neutron Star Masses. Physical Review Letters, 77, 1432.
https://doi.org/10.1103/PhysRevLett.77.1432

[35]   Gaztañaga, E., García-Berro, E., Isern, J., Bravo, E. and Domínguez, I. (2001) Bounds on the Possible Evolution of the Gravitational Constant from Cosmological Type-Ia Supernovae. Physical Review D, 65, 023506.

[36]   García-Berro, E., Kubyshin, Y., Loren-Aguilar, P. and Isern, J. (2006) The Variation of the Gravitational Constant Inferred from the Hubble Diagram of Type Ia Supernovae. International Journal of Modern Physics D, 15, 1163-1174.

[37]   García-Berro, J.I. and Kubyshin, Y.A. (2007) Astronomical Measurements and Constraints on the Variability of Fundamental Constants. The Astronomy and Astrophysics Review, 14, 113-170.

[38]   Corda, C. (2009) Interferometric Detection of Gravitational Waves: The Definitive Test for General Relativity. International Journal of Modern Physics D, 18, 2275.
https://doi.org/10.1142/S0218271809015904

[39]   https://www.ligo.org/detections/GW150914.php

[40]   https://www.ligo.org/detections/GW170817.php

[41]   Freedman, W.L., Madore, B.F., Scowcroft, V., et al. (2012) Carnegie Hubble Program: A Mid-Infrared Calibration of the Hubble Constant. ApJ, 758, 24.

[42]   Tammann, G.A. and Reindl, B. (2013) The Luminosity of Supernovae of Type Ia from Tip of the Red-Giant Branch Distances and the Value of H0. A&A, 549, A136.

 
 
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