Preview

Proceedings of the National Academy of Sciences of Belarus. Physics and Mathematics Series

Advanced search

An approach to the theory of gravity with an arbitrary reference level of energy density

https://doi.org/10.29235/1561-2430-2019-55-1-83-96

Abstract

Five-vectors theory of gravity is proposed, which admits an arbitrary choice of the energy density reference level. This theory is formulated as the constraint theory, where the Lagrange multipliers turn out to be restricted to some class of vector fields unlike the General Relativity (GR), where they are arbitrary. A possible cosmological implication of the proposed model is that the residual vacuum fluctuations dominate during the whole evolution of the universe. That resembles
the universe having a nearly linear dependence of a scale factor on cosmic time.

About the Authors

S. L. Cherkas
Institute for Nuclear Problems, Belarusian State University .
Belarus

 Ph. D. (Physics and Mathematics), Senior Researcher.

11, Bobruiskaya Str., 220050, Minsk.



V. L. Kalashnikov
Institute of Photonics, Vienna University of Technology.
Austria

 Ph. D. (Physics and Mathematics), Senior Researcher.

27/387, Gusshausstrasse, A-1040, Vienna.



References

1. Capozziello S., Faraoni V. Beyond Einstein Gravity. Dordrecht, Springer, 2011. 467 p. https://doi.org/10.1007/978-94-007-0165-6

2. Vladimirov Yu. S. Geomertofizika. Moscow, Binom Publ., 2012. 536 p. (in Russian).

3. DeWitt B. S. Quantum Theory of Gravity. I. The Canonical Theory. Physical Review, 1967, vol. 160, no. 5. pp.1113–1148. https://doi.org/10.1103/PhysRev.160.1113

4. Wheeler J. A., Superspace and nature of quantum geometrodynamics. DeWitt C., Wheeler J. A. (eds.). Battelle Rencontres, New York, Benjamin, 1968, pp. 242–308.

5. Ashtekar A., Stachel J. (eds.). Conceptual Problems of Quantum Gravity. Boston, Birkhäuser, 1991. 604 p.

6. Shestakova T. P., Simeone C. The problem of time and gauge invariance in the quantization of cosmological models. I. Canonical quantization methods. Gravitation and Cosmology, 2004, vol. 10, pp. 161–176.

7. Kiefer C. Quantum cosmology: expectations and results. Annalen der Physik, 2006, vol. 15, no. 4–5, pp. 316–325. https://doi.org/10.1002/andp.200510190

8. Mukhi S. String theory: a perspective over the last 25 years. Classical and Quantum Gravity, 2011, vol. 28, no. 15, p. 153001. https://doi.org/10.1088/0264-9381/28/15/153001

9. Ashtekar A., Gupt B. Generalized effective description of loop quantum cosmology. Physical Review D, 2015, vol. 92, no. 8–15, p. 084060. https://doi.org/10.1103/PhysRevD.92.084060

10. Jizba P., Kleinert H., Scardigli F. Inflationary cosmology from quantum Conformal Gravity. The European Physical Journal C, 2015, vol. 75, no. 6, p. 245. https://doi.org/10.1140/epjc/s10052-015-3441-6

11. Milne E. A., Relativity, Gravitation and World-Structure. Oxford, The Clarendon Press, 1935. 385 p.

12. Horava P. Quantum gravity at a Lifshitz point. Physical Review D, 2009, vol. 79, no. 8–15, p. 084008. https://doi.org/10.1103/PhysRevD.79.084008

13. Gomes H., Koslowski T. The link between general relativity and shape dynamics. Classical and Quantum Gravity, 2012, vol. 29, no. 7, p. 075009. https://doi.org/10.1088/0264-9381/29/7/075009

14. Ferreira P. G., Starkman G. D. Einstein's Theory of Gravity and the Problem of Missing Mass. Science. 2009, vol. 326, no. 5954, p. 812. https://doi.org/10.1126/science.1172245

15. Smolin L. Quantization of unimodular gravity and the cosmological constant problems. Physical Review D, 2009, vol. 80, no. 8–15, p. 084003. https://doi.org/10.1103/PhysRevD.80.084003

16. Milne E. A., Kinematic Relativity. Oxford the Clarendon Press, 1948. 247 p.

17. Landau L. D., Lifshitz E. M. The Classical Theory of Fields. Oxford, Butterworth-Heinemann, 2000. 428 p.

18. Arnowitt R., Deser S., Misner C. W. The Dynamics of General Relativity. Witten L. (ed.). Gravitation: an introduction to current research. New York, Wiley, 1962, chap. 7, p. 227.

19. Gitman D. M., Tyutin I. V. Quantization of Fields with Constraints. Berlin, Springer, 1990. 294 p.

20. Henneaux M., Teitelboim C. Quantization of Gauge Systems. Princeton, Princeton Univ. Pr., 1992. 514 p.

21. Cherkas S. L., Kalashnikov V. L. Quantization of the inhomogeneous Bianchi I model: quasi-Heisenberg picture. Nonlinear Phenomena in Complex Systems, 2015, vol. 18, pp. 1–14.

22. Yoneda G., Shinkai H. Constraint propagation in the family of ADM systems. Physical Review D, 2001, vol. 63, no. 12–15, p. 124019. https://doi.org/10.1103/PhysRevD.63.124019

23. Papapetrou A. Equations of motion in General Relativity. Proceedings of the Physical Society. Section A, vol. 64, no. 1, pp. 57–75. https://doi.org/10.1088/0370-1298/64/1/310

24. Infeld L. Equations of Motion in General Relativity Theory and the Action Principle. Reviews of Modern Physics, vol. 29, no. 3 pp. 398–411. https://doi.org/10.1103/revmodphys.29.398

25. Fock V. The Theory of Space, Time and Gravity. Oxford, Pergamon Press, 1966. 427 p. https://doi.org/10.1016/C2013-0-05319-4

26. Einstein A., Infeld L. On the motion of particles in general relativity theory. Canadian Journal of Mathematics, vol. 1, no. 3, pp. 209–241. https://doi.org/10.4153/cjm-1949-020-8

27. Katanaev M. O. Point massive particle in General Relativity. General Relativity and Gravitation, vol. 45, no. 10, pp. 1861–1875. https://doi.org/10.1007/s10714-013-1564-3

28. Commins E. D., Bucksbaum P. H. Weak Interactions of Leptons and Quarks. Cambridge, Cambridge Univ. Press, 1983. 473 p.

29. Arbuzov A. B., Barbashov B. M., Nazmitdinov R. G., Pervushin V. N., Borowiec A., Pichugin K. N., Zakharov A. F. Conformal Hamiltonian Dynamics of General Relativity. Physics Letters B, 2010, vol. 691, no. 5, pp. 230–230. https://doi.org/10.1016/j.physletb.2010.06.042

30. Alberghi G. L., Kamenshchik A. Yu., Tronconi A., Vacca G. P., Venturi G., Vacuum energy, cosmological constant and Standard Model physics. JETP Letters, 2008, vol. 88, no. 11, pp. 705–710. https://doi.org/10.1134/s002136400823001x

31. Copeland E. J. Dark energy in light of the discovery of the Higgs. Annalen der Physik, 2016, vol. 528, no. 1–2, pp. 62–67. https://doi.org/10.1002/andp.201500163

32. Dvali G., Gomez C. Quantum exclusion of positive cosmological constant? Annalen der Physik, vol. 528, no. 1–2, pp. 68–73. https://doi.org/10.1002/andp.201500216

33. Cherkas S. L., Kalashnikov V. L. Determination of the UV cut-off from the observed value of the Universe acceleration. Journal of Cosmology and Astroparticle Physics, 2007, vol. 1, p. 028. https://doi.org/10.1088/1475-7516/2007/01/028

34. Cherkas, S. L., Kalashnikov V. L. Universe driven by the vacuum of scalar field: VFD model. Baryshev, Yu. V., Taganov, I. N., Teerikorpi P. (eds.). Practical cosmology: proceedings of the International conference “Problems of practical cosmology”, held at Russian geographical society, 23-27 June 2008, vol. 2. Saint-Petersburg, Russ. geogr. soc., 2008, pp. 135–140.

35. Birrell N. D., Davis P. C. W. Quantum Fields in Curved Space. Cambridge, Cambridge Univ. Press, 1982. 352 p. https://doi.org/10.1017/CBO9780511622632

36. Gong Y., Wang A. Observational constraints on the acceleration of the Universe. Physical Review D, 2006, vol. 73, no. 8–15, p. 083506. https://doi.org/10.1103/PhysRevD.73.083506

37. Singh P., Lohiya D. Constraints on Lepton Asymmetry from Nucleosynthesis in a Linearly Coasting Cosmology. Journal of Cosmology and Astroparticle Physics, 2015, vol. 05, p. 061. https://doi.org/10.1088/1475-7516/2015/05/061

38. Dev A., Safonova M., Jain D., Lohiya D. Cosmological Tests for a Linear Coasting Cosmology. Physics Letters B, vol. 548, no. 1–2, pp. 12–18. https://doi.org/10.1016/S0370-2693(02)02814-9

39. Benoit-Lévy A., Chardin G. The Dirac-Milne cosmology. International Journal of Modern Physics: Conference Series, 2014, vol. 30, p. 1460272. https://doi.org/10.1142/S2010194514602725

40. Melia F. On recent claims concerning the Rh = ct Universe. Monthly Notices of the Royal Astronomical Society, 2015, vol. 446, no. 2, pp.1191–1194. https://doi.org/10.1093/mnras/stu2181

41. Shafer D. L. Robust model comparison disfavors power law cosmology. Physical Review D, 2015, vol. 91, no. 10, p. 103516. https://doi.org/10.1103/physrevd.91.103516

42. Melia F. The Linear Growth of Structure in the Rh = ct Universe. Monthly Notices of the Royal Astronomical Society, 2017,

43. vol. 464, no 2, pp. 1966–1976. https://doi.org/10.1093/mnras/stw2493

44. Bengochea G. R., Leon G. Puzzling initial conditions in the Rh = ct model. The European Physical Journal C, 2016, vol. 76, no. 11, p. 626. https://doi.org/10.1140/epjc/s10052-016-4485-y

45. Tutusaus I., Lamine B., Blanchard A., Dupays A., Zolnierowski Y, Cohen-Tanugi J., Ealet A., Escoffer S., Le Fèvre O., Ilić S., Pisani A., Plaszczynski S., Sakr Z., Salvatelli V., Schücker T., Tilquin A., Virey J.-M. Power law cosmology model comparison with CMB scale information. Physical Review D, 2016, vol. 94, no. 10, p. 103511. https://doi.org/10.1103/PhysRevD.94.103511


Review

Views: 893


Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 License.


ISSN 1561-2430 (Print)
ISSN 2524-2415 (Online)