Skip to main content
SpringerLink
Log in

Power-Law Inflation in Spacetimes Without Symmetry

  • Published:
Communications in Mathematical Physics Aims and scope Submit manuscript

Abstract

We consider models of accelerated cosmological expansion described by the Einstein equations coupled to a nonlinear scalar field with a suitable exponential potential. We show that homogeneous and isotropic solutions are stable under small nonlinear perturbations without any symmetry assumptions. Our proof is based on results on the nonlinear stability of de Sitter spacetime and Kaluza-Klein reduction techniques.

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. Anderson M.T. (2005) Existence and stability of even dimensional asymptotically de Sitter spaces. Ann. H. Poincaré 6, 801–820

    Article  MATH  Google Scholar 

  2. Bieli R. (2005) Algebraic expansions for curvature coupled scalar field models. Class. Quart. Grav. 22: 4363–4376

    Article  MATH  MathSciNet  ADS  Google Scholar 

  3. Choquet-Bruhat Y., DeWitt-Morette C. (1989) Analysis, Manifolds and Physics. Part 2. Amsterdam, North-Holland

    Google Scholar 

  4. Dobarro F., Ünal B. (2005) Curvature of multiply warped products. J. Geom. Phys. 55(1): 75–106

    Article  MATH  MathSciNet  Google Scholar 

  5. Friedrich H. (1986) Existence and structure of past asymptotically simple solutions of Einstein’s field equations with positive cosmological constant. J. Geom. Phys. 3, 101–117

    Article  MATH  MathSciNet  Google Scholar 

  6. Friedrich H. (1986) On the Existence of n-Geodesically Complete or Future Complete Solutions of Einstein’s Field Equations with Smooth Asymptotic Structure. Commun. Math. Phys. 107, 587–609

    Article  MATH  MathSciNet  ADS  Google Scholar 

  7. Halliwell J.J. (1987) Scalar fields in cosmology with an exponential potential. Phys. Lett. B 185, 341–344

    Article  MathSciNet  ADS  Google Scholar 

  8. Lee H. (2005) The Einstein-Vlasov system with a scalar field. Ann. Henri Poincaré 6, 697–723

    Article  MATH  Google Scholar 

  9. Müller V., Schmidt H.J., Starobinsky A.A. (1990) Power-law inflation as an attractor solution for inhomogeneous cosmological models. Class. Quant. Grav. 7, 1163–1168

    Article  ADS  Google Scholar 

  10. Rendall A.D. (2004) Accelerated cosmological expansion due to a scalar field whose potential has a positive lower bound. Class. Quant. Grav. 21, 2445–2454

    Article  MATH  MathSciNet  ADS  Google Scholar 

  11. Rendall A.D. (2004) Asymptotics of Solutions of the Einstein Equations with Positive Cosmological Constant. Ann. Henri Poincaré 5, 1041–1064

    Article  MATH  MathSciNet  Google Scholar 

  12. Rendall, A.D.: Mathematical properties of cosmological models with accelerated expansion. In: Lect. Notes in Phys. 692, Berlin-Heidelberg-New York: Springer, 2006, pp. 141–155

  13. Rendall A.D. (2005) Intermediate inflation and the slow-roll approximation. Class. Quant. Grav. 22, 1655–1666

    Article  MATH  MathSciNet  ADS  Google Scholar 

  14. Tchapnda S.B., Rendall A.D. (2003) Global existence and asymptotic behaviour in the future for the Einstein-Vlasov system with positive cosmological constant. Class. Quant. Grav. 20: 3037–3049

    Article  MATH  MathSciNet  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Max Planck Institute for Gravitational Physics, Albert Einstein Institute, Am Mühlenberg 1, D-14476, Golm, Germany

    J. Mark Heinzle & Alan D. Rendall

Authors
  1. J. Mark Heinzle
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Alan D. Rendall
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to J. Mark Heinzle.

Additional information

Communicated by G.W. Gibbons.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Heinzle, J.M., Rendall, A.D. Power-Law Inflation in Spacetimes Without Symmetry. Commun. Math. Phys. 269, 1–15 (2007). https://doi.org/10.1007/s00220-006-0133-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00220-006-0133-y

Keywords

Search

Navigation