Skip to main content
Log in

Singularity Crossing, Transformation of Matter Properties and the Problem of Parametrization in Field Theories

  • Published:
Foundations of Physics Aims and scope Submit manuscript

Abstract

We investigate particular cosmological models, based either on tachyon fields or on perfect fluids, for which soft future singularities arise in a natural way. Our main result is the description of a smooth crossing of the soft singularity in models with an anti-Chaplygin gas or with a particular tachyon field in the presence of dust. Such a crossing is made possible by certain transformations of matter properties. We discuss and compare also different approaches to the problem of crossing of the Big Bang–Big Crunch singularities.

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

Access this article

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. Lifshitz, E.M., Khalatnikov, I.M.: Investigations in relativistic cosmology. Adv. Phys. 12, 185 (1963)

    Article  ADS  MathSciNet  Google Scholar 

  2. Hawking, S.W., Penrose, R.: The singularities of gravitational collapse and cosmology. Proc. R. Soc. Lond. A 314, 529 (1970)

    Article  ADS  MathSciNet  Google Scholar 

  3. Penrose, R.: Structure of Space-Time. Benjamin, New York (1970)

    MATH  Google Scholar 

  4. Belinsky, V.A., Khalatnikov, I.M., Lifshitz, E.M.: Oscillatory approach to a singular point in the relativistic cosmology. Adv. Phys. 19, 525 (1970)

    Article  ADS  Google Scholar 

  5. Misner, C.W.: Mixmaster universe. Phys. Rev. Lett. 22, 1071 (1969)

    Article  ADS  Google Scholar 

  6. Barrow, J.D., Galloway, G.J., Tipler, F.J.: The closed-universe recollapse conjecture. Mon. Not. R. Astron. Soc. 223, 835 (1986)

    Article  ADS  Google Scholar 

  7. Riess, A., et al.: Observational evidence from supernovae for an accelerating universe and a cosmological constant. Astron. J. 116, 1009 (1998)

    Article  ADS  Google Scholar 

  8. Perlmutter, S.J., et al.: Measurements of Omega and Lambda from 42 high redshift supernovae. Astrophys. J. 517, 565 (1999)

    Article  ADS  Google Scholar 

  9. Sahni, V., Starobinsky, A.A.: Reconstructing dark energy. Int. J. Mod. Phys. D 15, 2105 (2006)

    Article  ADS  MathSciNet  Google Scholar 

  10. Kamenshchik, A.Y.: Quantum cosmology and late-time singularities. Class. Quantum Grav. 30, 173001 (2013)

    Article  ADS  MathSciNet  Google Scholar 

  11. Fernandez-Jambrina, L., Lazkoz, R.: Geodesic behaviour of sudden future singularities. Phys. Rev. D 70, 121503 (2004)

    Article  ADS  MathSciNet  Google Scholar 

  12. Fernandez-Jambrina, L., Lazkoz, R.: Classification of cosmological milestones. Phys. Rev. D 74, 064030 (2006)

    Article  ADS  MathSciNet  Google Scholar 

  13. Keresztes, Z., Gergely, L.A., Kamenshchik, A.Y., Gorini, V., Polarski, D.: Soft singularity crossing and transformation of matter properties. Phys. Rev. D 88, 023535 (2013)

    Article  ADS  Google Scholar 

  14. Sen, A.: Rolling tachyon. J. High Energy Phys. 04, 048 (2002)

    Article  ADS  MathSciNet  Google Scholar 

  15. Padmanabhan, T.: Accelerated expansion of the universe driven by tachyonic matter. Phys. Rev. D 66, 021301 (2002)

    Article  ADS  Google Scholar 

  16. Feinstein, A.: Power law inflation from the rolling tachyon. Phys. Rev. D 66, 063511 (2002)

    Article  ADS  Google Scholar 

  17. Born, M., Infeld, L.: Foundations of the new field theory. Proc. R. Soc. Lond. A 144, 425 (1934)

    Article  ADS  Google Scholar 

  18. Gorini, V., Kamenshchik, A.Y., Moschella, U., Pasquier, V.: Tachyons, scalar fields and cosmology. Phys. Rev. D 69, 123512 (2004)

    Article  ADS  MathSciNet  Google Scholar 

  19. Bars, I., Chen, S.H., Steinhardt, P.J., Turok, N.: Antigravity and the big crunch/big bang transition. Phys. Lett. B 715, 278 (2012)

    Article  ADS  Google Scholar 

  20. Bars, I., Steinhardt, P., Turok, N.: Sailing through the big crunch-big bang transition. Phys. Rev. D 89, 061302 (2014)

    Article  ADS  Google Scholar 

  21. Wetterich, C.: Variable gravity universe. Phys. Rev. D 89, 024005 (2014)

    Article  ADS  Google Scholar 

  22. Wetterich, C.: Eternal universe. Phys. Rev. D 90, 043520 (2014)

    Article  ADS  Google Scholar 

  23. Dominis Prester, P.: Curing black hole singularities with local scale invariance. Adv. Math. Phys. 2016, 6095236 (2016)

    Article  MathSciNet  Google Scholar 

  24. Dominis Prester, P.: Field redefinitions, Weyl invariance and the nature of mavericks. Class. Quantum Grav. 31, 155006 (2014)

    Article  ADS  MathSciNet  Google Scholar 

  25. Keresztes, Z., Gergely, L.A., Kamenshchik, A.Y., Gorini, V., Polarski, D.: Will the tachyonic universe survive the big brake? Phys. Rev. D 82, 123534 (2010)

    Article  ADS  Google Scholar 

  26. Carter, B.: Duality relation between charged elastic strings and superconducting cosmic strings. Phys. Lett. B 224, 61 (1989)

    Article  ADS  MathSciNet  Google Scholar 

  27. Vilenkin, A.: Effect of small scale structure on the dynamics of cosmic strings. Phys. Rev. D 41, 3038 (1990)

    Article  ADS  Google Scholar 

  28. Keresztes, Z., Gergely, L.A., Kamenshchik, A.Y.: Paradox of soft singularity crossing and its resolution by distributional cosmological quantities. Phys. Rev. D 86, 063522 (2012)

    Article  ADS  Google Scholar 

  29. Kamenshchik, A.Y., Moschella, U., Pasquier, V.: An alternative to quintessence. Phys. Lett. B 511, 265 (2001)

    Article  ADS  Google Scholar 

  30. Frolov, A.V., Kofman, L., Starobinsky, A.A.: Prospects and problems of tachyon matter cosmology. Phys. Lett. B 545, 8 (2002)

    Article  ADS  Google Scholar 

  31. Kamenshchik, A.Y., Pozdeeva, E.O., Vernov, S.Y., Tronconi, A., Venturi, G.: Transformations between Jordan and Einstein frames: bounces, antigravity, and crossing singularities. Phys. Rev. D 94, 063510 (2016)

    Article  ADS  MathSciNet  Google Scholar 

  32. Wagoner, R.V.: Scalar tensor theory and gravitational waves. Phys. Rev. D 1, 3209 (1970)

    Article  ADS  Google Scholar 

  33. Kamenshchik, A.Y., Pozdeeva, E.O., Tronconi, A., Venturi, G., Vernov, S.Y.: Integrable cosmological models with non-minimally coupled scalar fields. Class. Quantum Grav. 31, 105003 (2014)

    Article  ADS  MathSciNet  Google Scholar 

  34. Kamenshchik, A.Y., Pozdeeva, E.O., Tronconi, A., Venturi, G., Vernov, S.Y.: Interdependence between integrable cosmological models with minimal and non-minimal coupling. Class. Quantum Grav. 33, 015004 (2016)

    Article  ADS  MathSciNet  Google Scholar 

  35. Fre, P., Sagnotti, A., Sorin, A.S.: Integrable scalar cosmologies I. Foundations and links with string theory. Nucl. Phys. B 877, 1028 (2013)

    Article  ADS  MathSciNet  Google Scholar 

  36. Sakharov, A.D.: Vacuum quantum fluctuations in curved space and the theory of gravitation. Sov. Phys. Dokl. 12, 1040 (1968)

    ADS  Google Scholar 

  37. Cooper, F., Venturi, G.: Cosmology and broken scale invariance. Phys. Rev. D 24, 3338 (1981)

    Article  ADS  MathSciNet  Google Scholar 

  38. Steinwachs, C.F., Kamenshchik, A.Y.: One-loop divergences for gravity non-minimally coupled to a multiplet of scalar fields: calculation in the Jordan frame. I. The main results. Phys. Rev. D 84, 024026 (2011)

    Article  ADS  Google Scholar 

  39. Kamenshchik, A.Y., Steinwachs, C.F.: Question of quantum equivalence between Jordan frame and Einstein frame. Phys. Rev. D 91, 084033 (2015)

    Article  ADS  Google Scholar 

  40. Kamenshchik, A.Y., Pozdeeva, E.O., Tronconi, A., Venturi, G., Vernov, S.Y.: Integrable cosmological models with non-minimally coupled scalar fields. Class. Quantum Grav. 31, 105003 (2014)

    Article  ADS  MathSciNet  Google Scholar 

  41. Kamenshchik, A., Tronconi, A., Venturi, G.: Reconstruction of scalar potentials in induced gravity and cosmology. Phys. Lett. B 702, 191 (2011)

    Article  ADS  Google Scholar 

  42. Lucchin, F., Matarrese, S.: Power law inflation. Phys. Rev. D 32, 1316 (1985)

    Article  ADS  Google Scholar 

  43. Gasperini, M., Veneziano, G.: The Pre-big bang scenario in string cosmology. Phys. Rep. 373, 1 (2003)

    Article  ADS  MathSciNet  Google Scholar 

  44. Boisseau, B., Giacomini, H., Polarski, D.: Scalar field cosmologies with inverted potentials. J. Cosmol. Astropart. Phys. 1510, 033 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  45. Starobinsky, A.A.: Can the effective gravitational constant become negative? Sov. Astron. Lett. 7, 36 (1981)

    ADS  Google Scholar 

  46. Linde, A.D.: Gauge theories and variability of the gravitational constant in the early universe. JETP Lett. 30, 447 (1980)

    ADS  Google Scholar 

  47. Kamenshchik, A.Y., Pozdeeva, E.O., Vernov, S.Y., Tronconi, A., Venturi, G.: Bianchi-I cosmological model and crossing singularities. Phys. Rev. D 95, 083503 (2017)

    Article  ADS  MathSciNet  Google Scholar 

  48. Chimento, L.P.: General solution to two-scalar field cosmologies with exponential potentials. Class. Quantum Grav. 15, 965 (1998)

    Article  ADS  MathSciNet  Google Scholar 

  49. Russo, J.G.: Exact solution of scalar tensor cosmology with exponential potentials and transient acceleration. Phys. Lett. B 600, 185 (2004)

    Article  ADS  MathSciNet  Google Scholar 

  50. Elizalde, E., Nojiri, S., Odintsov, S.D.: Exact solution of scalar tensor cosmology with exponential potentials and transient acceleration. Phys. Rev. D 70, 043539 (2004)

    Article  ADS  Google Scholar 

  51. Rubano, C., Scudellaro, P., Piedipalumbo, E., Capozziello, S., Capone, M.: Exponential potentials for tracker fields. Phys. Rev. D 69, 103510 (2004)

    Article  ADS  Google Scholar 

  52. Andrianov, A.A., Cannata, F., Kamenshchik, A.Y.: General solution of scalar field cosmology with a (piecewise) exponential potential. J. Cosmol. Astropart. Phys. 1110, 004 (2011)

    Article  ADS  Google Scholar 

  53. Piedipalumbo, E., Scudellaro, P., Esposito, G., Rubano, C.: On quintessential cosmological models and exponential potentials. General Relat. Gravit. 44, 2611 (2012)

    Article  ADS  MathSciNet  Google Scholar 

  54. Carrasco, J.J.M., Chemissany, W., Kallosh, R.: Journeys through antigravity? J. High Energy Phys. 1401, 130 (2014)

    Article  ADS  MathSciNet  Google Scholar 

  55. Kallosh, R., Linde, A.: Hidden superconformal symmetry of the cosmological evolution. J. Cosmol. Astropart. Phys. 1401, 020 (2014)

    Article  ADS  MathSciNet  Google Scholar 

  56. Penrose, R.: Cycles of Time: An Extraordinary New View of the Universe. Bodley Head, London (2010)

    MATH  Google Scholar 

  57. Anguige, K., Tod, K.P.: Isotropic cosmological singularities: I. Polytropic perfect fluid spacetimes. Ann. Phys. 276, 257 (1999)

    Article  ADS  MathSciNet  Google Scholar 

  58. Anguige, K., Tod, K.P.: Isotropic cosmological singularities: II. The Einstein–Vlasov system. Ann. Phys. 276, 294 (1999)

    Article  ADS  MathSciNet  Google Scholar 

  59. Tod, K.P.: Isotropic cosmological singularities: other matter models. Class. Quantum Grav. 20, 521 (2003)

    Article  ADS  MathSciNet  Google Scholar 

Download references

Acknowledgements

This work was partially supported by the RFBR Grant No. 17-02-01008.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to A. Yu. Kamenshchik.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kamenshchik, A.Y. Singularity Crossing, Transformation of Matter Properties and the Problem of Parametrization in Field Theories. Found Phys 48, 1159–1176 (2018). https://doi.org/10.1007/s10701-018-0161-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10701-018-0161-4

Keywords

Navigation