Abstract
We consider the dynamics of the universe following from the variational principle with boundary terms added to the action. We calculate a scalar function that effectively accounts for the contribution of these boundary terms to the density and pressure of the medium filling the universe. An interesting result of the proposed approach is that a superfast expansion stage arises automatically (without additional conditions). We show the connection between the description of inflationary expansion based on the scalar field and our model.
Similar content being viewed by others
References
S. Weinberg, Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity, John Wiley and Sons, New York (1972).
A. Riess et al., “Observational evidence from supernovae for an accelerating universe and a cosmological constant,” Astron. J., 116, 1009–1038 (1998); arXiv:astro-ph/9805201v1 (1998).
S. Perlmutter, G. Aldering, and G. Goldhaber, “Measurements of \(\Omega\) and \(\Lambda\) from 42 high-redshift supernovae,” Astrophys. J., 517, 565–586 (1999); arXiv:astro-ph/9812133v1 (1998).
Yu. L. Bolotin, D. A. Erokhin, and O. A. Lemets, “Expanding Universe: Slowdown or speedup?” Phys. Usp., 55, 876–918 (2012).
S. Carneiro, M. A. Dantas, C. Pigozzo, and J. S. Alcaniz, “Observational constraints on late-time \(\Lambda(t)\) cosmology,” Phys. Rev. D, 77, 083504 (2008); arXiv:0711.2686v2 [astro-ph] (2007).
M. Bronstein, “On the expanding universe,” Phys. Z. Sowjetunion, 3, 73–82 (1933).
M. Özer and M. O. Taha, “A possible solution to the main cosmological problems,” Phys. Lett. B, 171, 363–365 (1986).
K. Freese, F. C. Adams, J. A. Frieman, and E. Mottola, “Cosmology with decaying vacuum energy,” Nucl. Phys. B, 287, 797–814 (1987).
W. Chen and Y-S. Wu, “Implications of a cosmological constant varying as \(R^{-2}\),” Phys. Rev. D, 41, 695–698 (1990).
J. C. Carvalho, J. A. S. Lima, and I. Waga, “Cosmological consequences of a time-dependent \(\Lambda\) term,” Phys. Rev. D, 46, 2404–2407 (1992).
A.-M. M. Abdel-Rahman, “Singularity-free decaying-vacuum cosmologies,” Phys. Rev. D, 45, 3497–3511 (1992).
J. A. S. Lima and M. Trodden, “Decaying vacuum energy and deflationary cosmology in open and closed universes,” Phys. Rev. D, 53, 4280–4286 (1996); arXiv:astro-ph/9508049v1 (1995).
J. M. Overduin and F. I. Cooperstock, “Evolution of the scale factor with a variable cosmological term,” Phys. Rev. D, 58, 043506 (1998); arXiv:astro-ph/9805260v1 (1998).
C. S. Weinberg, “The cosmological constant problem,” Rev. Modern Phys., 61, 1–23 (1989).
G. W. Gibbons and S. W. Hawking, “Action integrals and partition functions in quantum gravity,” Phys. Rev. D, 15, 2752–2756 (1977).
Y.-F. Cai, J. Liu, and H. Li, “Entropic cosmology: A unified model of inflation and late-time acceleration,” Phys. Lett. B, 690, 213–219 (2010); arXiv:1003.4526v2 [astro-ph.CO] (2010).
D. A. Easson, P. H. Frampton, and G. F. Smoot, “Entropic accelerating universe,” Phys. Lett. B, 696, 273–277 (2011); arXiv:1002.4278v3 [hep-th] (2010).
C. A. Sporea, “Notes on \(f(R)\) theories of gravity,” arXiv:1403.3852v2 [gr-qc] (2014).
N. J. Poplawski, “Interacting dark energy in \(f(R)\) gravity,” Phys. Rev. D, 74, 084032 (2006); arXiv:gr-qc/0607124v3 (2006).
N. J. Poplawski, “A Lagrangian description of interacting dark energy,” arXiv:gr-qc/0608031v2 (2006).
S. Nojiri and S. D. Odintsov, “Unified cosmic history in modified gravity: From \(F(R)\) theory to Lorentz non-invariant models,” Phys. Rep., 505, 59–144 (2011); arXiv:1011.0544v4 [gr-qc] (2010).
A. Linde, “Inflation, quantum cosmology, and the anthropic principle,” in: Science and Ultimate Reality: Quantum Theory, Cosmology, and Complexity (J. D. Barrow, P. C. W. Davies, and C. L. Harper Jr., eds.), Cambridge Univ. Press, Cambridge (2011), pp. 426–458; arXiv:hep-th/0211048v2 (2002).
S. V. Chernov, I. V. Fomin, and A. Beesham, “The method of generating functions in exact scalar field cosmology,” Eur. Phys. J. C, 78, 301 (2018); arXiv:1704.08712v2 [gr-qc] (2017).
V. Poulin, T. L. Smith, T. Karwal, and M. Kamionkowski, “Early dark energy can resolve the Hubble tension,” Phys. Rev. Lett., 122, 221301 (2019); arXiv:1811.04083v2 [astro-ph.CO] (2018).
Acknowledgments
The author is grateful to Yu. V. Pavlov, S. A. Paston, and S. M. Gerasyuta for the useful discussions during the writing of this paper.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
The author declares no conflicts of interest.
Rights and permissions
About this article
Cite this article
Kochkin, V.I. Dynamics of the Friedmann universe with boundary terms added to the action. Theor Math Phys 206, 236–242 (2021). https://doi.org/10.1134/S0040577921020094
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0040577921020094