- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review D

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Classes of nonminimally coupled scalar fields in spatially curved FRW spacetimes

Morteza Kerachian1,*, Giovanni Acquaviva1,†, and Georgios Lukes-Gerakopoulos2,‡

  • 1Institute of Theoretical Physics, Faculty of Mathematics and Physics, Charles University, CZ-180 00 Prague, Czech Republic
  • 2Astronomical Institute of the Academy of Sciences of the Czech Republic, Boční II 1401/1a, CZ-141 00 Prague, Czech Republic

  • *morteza.kerachian@gmail.com
  • †gioacqua@gmail.com
  • ‡gglukes@gmail.com
PDF

Phys. Rev. D 99, 123516 – Published 14 June, 2019

DOI: https://doi.org/10.1103/PhysRevD.99.123516

Abstract

In this work we perform a dynamical analysis of a broad class of nonminimally coupled real scalar fields in the Friedmann-Robertson-Walker (FRW) spacetime framework. The first part of our study concerns the dynamics of an unspecified positive potential in a spatially curved FRW spacetime, for which we define a new set of dimensionless variables and a new evolution parameter. In the framework of this general setup, we have recognized several general features of the system, like symmetries, invariant subsets and critical points, and provide their cosmological interpretation. The second part of our work focuses on flat FRW cases for which the tracker parameter is constant; i.e., we examine specific classes of potentials. After analyzing these cases dynamically, we discuss their physical interpretation.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (34)

  1. A. A. Starobinsky, Spectrum of relict gravitational radiation and the early state of the universe, JETP Lett. 30, 682 (1979).
  2. A. H. Guth, Inflationary universe: A possible solution to the horizon and flatness problems, Phys. Rev. D 23, 347 (1981).
  3. A. D. Linde, A new inflationary universe scenario: A possible solution of the horizon, flatness, homogeneity, isotropy and primordial monopole problems, Phys. Lett. 108B, 389 (1982).
  4. Y. Akrami et al. (Planck Collaboration), Planck 2018 results. x. Constraints on inflation, arXiv:1807.06211.
  5. A Albrecht and P. J. Steinhardt, Cosmology for Grand Unified Theories with Radiatively Induced Symmetry Breaking, Phys. Rev. Lett. 48, 1220 (1982).
  6. L. Kofman, A. Linde, and A. A. Starobinsky, Reheating after Inflation, Phys. Rev. Lett. 73, 3195 (1994).
  7. E. W. Kolb and M. S. Turner, The early universe, Front. Phys. Vol. 69 (1990), http://inspirehep.net/record/299778?ln=en.
  8. M. Galante, R. Kallosh, A. Linde, and D. Roest, Unity of Cosmological Inflation Attractors, Phys. Rev. Lett. 114, 141302 (2015).
  9. N. Aghanim, Y. Akrami, M. Ashdown, J. Aumont, C. Baccigalupi, M. Ballardini, A. J. Banday, R. B. Barreiro, N. Bartolo, S. Basak et al., Planck 2018 results. vi. Cosmological parameters, arXiv:1807.06209.
  10. I. Zlatev, L. Wang, and P. J. Steinhardt, Quintessence, Cosmic Coincidence, and the Cosmological Constant, Phys. Rev. Lett. 82, 896 (1999).
  11. E. J. Copeland, M. Sami, and S. Tsujikawa, Dynamics of dark energy, Int. J. Mod. Phys. D 15, 1753 (2006).
  12. L. Amendola, Cosmology with nonminimal derivative couplings, Phys. Lett. B 301, 175 (1993).
  13. S. V. Sushkov, Exact cosmological solutions with nonminimal derivative coupling, Phys. Rev. D 80, 103505 (2009).
  14. E. N. Saridakis and S. V. Sushkov, Quintessence and phantom cosmology with nonminimal derivative coupling, Phys. Rev. D 81, 083510 (2010).
  15. B. Allen, Phase transitions in de sitter space, Nucl. Phys. B226, 228 (1983).
  16. N. D. Birrel and P. Davies, Quantum fields in curved space (Cambridge University Press, New York, Melbourne, 1982), p. 340, https://ui.adsabs.harvard.edu/abs/1982qfcs.book..340B/abstract.
  17. K.-i. Maeda, Stability and attractor in a higher-dimensional cosmology. i, Classical Quantum Gravity 3, 233 (1986).
  18. F. S. Accetta, D. J. Zoller, and M. S. Turner, Induced-gravity inflation, Phys. Rev. D 31, 3046 (1985).
  19. F. Bezrukov and M. Shaposhnikov, The standard model higgs boson as the inflaton., Phys. Lett. B 659, 703 (2008).
  20. G. Aad et al. (ATLAS Collaboration), Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC, Phys. Lett. B 716, 1 (2012).
  21. V. Faraoni, Conformally coupled inflation, Galaxies 1, 96 (2013).
  22. A. Barroso, J. Casasayas, P. Crawford, P. Moniz, and A. Nunes, Inflation in the presence of a non-minimal coupling, Phys. Lett. B 275, 264 (1992).
  23. J.-P. Uzan, Cosmological scaling solutions of nonminimally coupled scalar fields, Phys. Rev. D 59, 123510 (1999).
  24. E. Gunzig, V. Faraoni, A. Figueiredo, T. M. Rocha Filho, and L. Brenig, The dynamical system approach to scalar field cosmology, Classical Quantum Gravity 17, 1783 (2000).
  25. O. Bertolami and P. J. Martins, Nonminimal coupling and quintessence, Phys. Rev. D 61, 064007 (2000).
  26. R. de Ritis, A. A. Marino, C. Rubano, and P. Scudellaro, Tracker fields from nonminimally coupled theory, Phys. Rev. D 62, 043506 (2000).
  27. A. Riazuelo and J.-P. Uzan, Cosmological observations in scalar-tensor quintessence, Phys. Rev. D 66, 023525 (2002).
  28. O. Hrycyna and M. Szydłowski, Uniting cosmological epochs through the twister solution in cosmology with non-minimal coupling, J. Cosmol. Astropart. Phys. 12 (2010) 016.
  29. M. Sami, M. Shahalam, M. Skugoreva, and A. Toporensky, Cosmological dynamics of a nonminimally coupled scalar field system and its late time cosmic relevance, Phys. Rev. D 86, 103532 (2012).
  30. A. Y. Kamenshchik, E. O. Pozdeeva, A. Tronconi, G. Venturi, and S. Y. Vernov, Integrable cosmological models with non-minimally coupled scalar fields, Classical Quantum Gravity 31, 105003 (2014).
  31. M. A. Skugoreva, A. V. Toporensky, and S. Y. Vernov, Global stability analysis for cosmological models with nonminimally coupled scalar fields, Phys. Rev. D 90, 064044 (2014).
  32. O. Hrycyna, What ξ? cosmological constraints on the non-minimal coupling constant, Phys. Lett. B 768, 218 (2017).
  33. S. Bahamonde, C. G. Böhmer, S. Carloni, E. J. Copeland, W. Fang, and N. Tamanini, Dynamical systems applied to cosmology: Dark energy and modified gravity, Phys. Rep. 775, 1 (2018).
  34. O. Hrycyna and M. Szydłowski, Cosmological dynamics with nonminimally coupled scalar field and a constant potential function, J. Cosmol. Astropart. Phys. 11 (2015) 013.

Outline

Information

Phys. Rev. D 99, 123516– Published 14 June, 2019
  • Received 2 April 2019
Crossmark - Check for updates button

© 2019 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation