Skip to main content
SpringerLink
Log in

Integrable cosmological models in the Einstein and in the Jordan frames and Bianchi-I cosmology

  • The International Session-Conference of SNP PSD RAS “Physics of Fundamental Interactions” April 12–15, 2016, Dubna, Russia
  • Session 7—Gravitation and Cosmology
  • Published:
Physics of Particles and Nuclei Aims and scope Submit manuscript

Abstract

We study integrable models in the Bianchi I metric case with scalar fields minimally and non-minimally coupled with gravity and the correspondence between their general solutions. Using the model with a minimally coupled scalar field and a constant potential as an example, we demonstrate how to obtain the general solutions of the corresponding models in the Jordan frame.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. N. A. Chernikov and E. A. Tagirov, “Quantum theory of scalar fields in de Sitter space-time”, Annales Poincare Phys. Theor. A 9, 109 (1968), E. A. Tagirov, “Consequences of field quantization in de Sitter type cosmological models”, Annals Phys 76, 561 (1973).

    ADS  MathSciNet  MATH  Google Scholar 

  2. C. G. Callan, S. R. Coleman, and R. Jackiw, “A new improved energy–momentum tensor”, Annals Phys 59, 42 (1970).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  3. P. A. R. Ade et al. (Planck Collab.), Planck 2015 Results, XX. Constraints on inflation, Astron. Astrophys 594, A20 (2016); arXiv:1502.02114.

    Article  Google Scholar 

  4. B. L. Spokoiny, “Inflation and generation of perturbations in Broken symmetric theory of gravity”, Phys. Lett. B 147, 39–43 (1984), T. Futamase and K.-I. Maeda, “Chaotic inflationary scenario in models having nonminimal coupling with curvature”, Phys. Rev. D 39, 399–404 (1989), R. Fakir and W. G. Unruh, “Improvement on cosmological chaotic inflation through nonminimal coupling”, Phys. Rev. D 41, 1783–1791 (1990), M. V. Libanov, V. A. Rubakov, and P. G. Tinyakov, “Cosmology with nonminimal scalar field: Graceful entrance into inflation”, Phys. Lett. B 442, 63 (1998); arXiv:hep-ph/9807553, A. Cerioni, F. Finelli, A. Tronconi, and G. Venturi, “Inflation and reheating in induced gravity”, Phys. Lett. B 681, 383–386 (2009); arXiv:0906.1902, R. Kallosh, A. Linde, and D. Roest, “The double attractor behavior of induced inflation”, J. High Energy Phys. 1409, 062 (2014); arXiv:1407.4471, M. Rinaldi, L. Vanzo, S. Zerbini, and G. Venturi, “Inflationary quasi-scale invariant attractors”, Phys. Rev. D 93, 024040 (2016); arXiv:1505.03386.

    Article  ADS  Google Scholar 

  5. F. L. Bezrukov and M. Shaposhnikov, “The standard model Higgs boson as the inflaton”, Phys. Lett. B 659, 703 (2008); arXiv:0710.3755, A. O. Barvinsky, A. Y. Kamenshchik, and A. A. Starobinsky, “Inflation scenario via the standard model Higgs boson and LHC”, J. Cosmol. Astropart. Phys 0811, 021 (2008); arXiv:0809.2104, F. Bezrukov, D. Gorbunov, and M. Shaposhnikov, “On initial conditions for the Hot Big Bang”, J. Cosmol. Astropart. Phys 0906, 029 (2009); arXiv:0812.3622, A. O. Barvinsky, A. Y. Kamenshchik, C. Kiefer, A. A. Starobinsky, and C. F. Steinwachs, “Asymptotic freedom in inflationary cosmology with a nonminimally coupled Higgs field”, J. Cosmol. Astropart. Phys 0912, 003 (2009); arXiv:0904.1698, A. De Simone, M. P. Hertzberg, and F. Wilczek, “Running inflation in the standard model”, Phys. Lett. B 678, 1 (2009); arXiv:0812.4946, F. L. Bezrukov, A. Magnin, M. Shaposhnikov, and S. Sibiryakov, “Higgs inflation: Consistency and generalizations”, J. High Energy Phys 1101, 016 (2011); arXiv:1008.5157, A. O. Barvinsky, A. Yu. Kamenshchik, C. Kiefer, A. A. Starobinsky, and C. F. Steinwachs, “Higgs boson, renormalization group, and cosmology”, Eur. Phys. J. C 72, 2219 (2012); arXiv:0910.1041, F. Bezrukov, “The Higgs field as an inflaton”, Class. Quant. Grav 30, 214001 (2013); arXiv:1307.0708, J. Ren, Z.-Z. Xianyu, and H. J. He, “Higgs gravitational interaction, weak boson scattering, and Higgs inflation in Jordan and Einstein frames”, J. Cosmol. Astropart. Phys 1406, 032 (2014); arXiv:1404.4627.

    Article  ADS  Google Scholar 

  6. E. Elizalde, S. D. Odintsov, E. O. Pozdeeva, and S. Yu. Vernov, “Renormalization-group inflationary scalar electrodynamics and scenarios confronted with Planck2013 and BICEP2 results”, Phys. Rev. D 90, 084001 (2014); arXiv:1408.1285, T. Inagaki, R. Nakanishi, and S. D. Odintsov, “Non-minimal twoloop inflation”, Phys. Lett. B 745, 105 (2015); arXiv:1502.06301, E. Elizalde, S. D. Odintsov, E. O. Pozdeeva, and S. Yu. Vernov, “Cosmological attractor inflation from the RG-improved Higgs sector of finite Gauge theory”, J. Cosmol. Astropart. Phys 1602, 025 (2016); arXiv:1509.08817.

    Article  ADS  Google Scholar 

  7. A. Yu. Kamenshchik, E. O. Pozdeeva, A. Tronconi, G. Venturi, and S. Yu. Vernov, “Integrable cosmological models with non-minimally coupled scalar fields”, Class. Quant. Grav 31, 105003 (2014); arXiv:1307.1910.

    Article  ADS  MathSciNet  MATH  Google Scholar 

  8. A. Yu. Kamenshchik, E. O. Pozdeeva, A. Tronconi, G. Venturi, and S. Yu. Vernov, “Interdependence between integrable cosmological models with minimal and non-minimal coupling”, Class. Quant. Grav 33, 015004 (2016); arXiv:1509.00590.

    Article  ADS  MathSciNet  MATH  Google Scholar 

  9. A. Yu. Kamenshchik, E. O. Pozdeeva, A. Tronconi, G. Venturi, and S. Yu. Vernov, “Transformations between Jordan and Einstein frames: Bounces, antigravity, and crossing singularities”, Phys. Rev. D 94, 063510 (2016); arXiv:1602.07192, A. Yu. Kamenshchik, E. O. Pozdeeva, A. Tronconi, G. Venturi, and S. Yu. Vernov, “General solutions of integrable cosmological models with nonminimal coupling”, Phys. Part. Nucl. Lett. 14 (2017) 382–385; arXiv:1604.01959.

    Article  ADS  MathSciNet  Google Scholar 

  10. T. S. Pereira, C. Pitrou, and J.-Ph. Uzan, “Theory of cosmological perturbations in an anisotropic universe”, J. Cosmol. Astropart. Phys 0709, 006 (2007); arXiv:0707.0736.

    Article  ADS  Google Scholar 

  11. I. Ya. Aref’eva, N. V. Bulatov, L. V. Joukovskaya, and S. Yu. Vernov, “The NEC violation and classical stability in the Bianchi I metric”, Phys. Rev. D 80, 083532 (2009); arXiv:0903.5264.

    Article  ADS  MathSciNet  Google Scholar 

  12. I. Ya. Aref’eva, L. V. Joukovskaya, and S. Yu. Vernov, “Dynamics in nonlocal linear models in the Friedmann- Robertson-Walker metric”, J. Phys. A 41, 304003 (2008); arXiv:0711.1364.

    Article  MathSciNet  MATH  Google Scholar 

  13. A. Yu. Kamenshchik, E. O. Pozdeeva, A. Tronconi, G. Venturi, and S. Yu. Vernov, Work in progress.

  14. I. M. Khalatnikov and A. Yu. Kamenshchik, “A generalization of the Heckmann-Schucking cosmological solution”, Phys. Lett. B 553, 119 (2003); arXiv:grqc/0301022.

    Article  ADS  MathSciNet  MATH  Google Scholar 

  15. A. Yu. Kamenshchik and C. M. F. Mingarelli, “A generalized Heckmann-Schucking cosmological solution in the presence of a negative cosmological constant”, Phys. Lett. B 693, 213 (2010); arXiv:0909.4227.

    Article  ADS  MathSciNet  Google Scholar 

  16. P. Fre, A. Sagnotti, and A. S. Sorin, “Integrable scalar cosmologies, I: Foundations and links with string theory”, Nucl. Phys. B 877, 1028 (2013); arXiv:1307.1910.

    Article  ADS  MathSciNet  MATH  Google Scholar 

  17. T. Christodoulakis, T. Grammenos, C. Helias, P. G. Kevrekidis, and A. Spanou, “Decoupling of the general scalar field mode and the solution space for Bianchi type I and V cosmologies coupled to perfect fluid sources”, J. Math. Phys 47, 042505 (2006); arXiv:gr-qc/0506132, I. Bars, S. H. Chen, P. J. Steinhardt, and N. Turok, “Antigravity and the Big Crunch/Big Bang transition”, Phys. Lett. B 715, 278 (2012); arXiv:1112.2470, A. Yu. Kamenshchik, E. O. Pozdeeva, A. A. Starobinsky, A. Tronconi, G. Venturi, and S. Yu. Vernov, “Induced gravity, and minimally and conformally coupled scalar fields in Bianchi-I cosmological models”, arXiv:1710.02681.

    Article  ADS  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dipartimento di Fisica e Astronomia and INFN, Via Irnerio 46, Bologna, 40126, Italy

    A. Yu. Kamenshchik, A. Tronconi & G. Venturi

  2. Landau Institute for Theoretical Physics, Russian Academy of Sciences, Moscow, 119334, Russia

    A. Yu. Kamenshchik

  3. Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University, Moscow, 119991, Russia

    E. O. Pozdeeva & S. Yu. Vernov

Authors
  1. A. Yu. Kamenshchik
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. E. O. Pozdeeva
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. A. Tronconi
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. G. Venturi
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. S. Yu. Vernov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. Yu. Kamenshchik.

Additional information

The article is published in the original.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kamenshchik, A.Y., Pozdeeva, E.O., Tronconi, A. et al. Integrable cosmological models in the Einstein and in the Jordan frames and Bianchi-I cosmology. Phys. Part. Nuclei 49, 1–4 (2018). https://doi.org/10.1134/S1063779618010173

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1063779618010173

Search

Navigation