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On dynamical systems approaches and methods in f (R) cosmology
Univ Lisbon, Ctr Math Anal Geometry & Dynam Syst, Inst Super Tecn, Av Rovisco Pais, P-1049001 Lisbon, Portugal..ORCID iD: 0000-0002-5753-8333
Univ Lisbon, Ctr Multidisciplinar Astrofis CENTRA, Inst Super Tecn, Av Rovisco Pais, P-1049001 Lisbon, Portugal..
Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Engineering and Physics.
2016 (English)In: Journal of Cosmology and Astroparticle Physics, ISSN 1475-7516, E-ISSN 1475-7516, no 8, 064Article in journal (Refereed) Published
Abstract [en]

We discuss dynamical systems approaches and methods applied to flat Robertson Walker models in f(R)-gravity. We argue that a complete description of the solution space of a model requires a global state space analysis that motivates globally covering state space adapted variables. This is shown explicitly by an illustrative example, f(R) = R + alpha R-2, alpha > 0, for which we introduce new regular dynamical systems on global compactly extended state spaces for the Jordan and Einstein frames. This example also allows us to illustrate several local and global dynamical systems techniques involving, e.g., blow ups of nilpotent fixed points, center manifold analysis, averaging, and use of monotone functions. As a result of applying dynamical systems methods to globally state space adapted dynamical systems formulations, we obtain pictures of the entire solution spaces in both the Jordan and the Einstein frames. This shows, e.g., that due to the domain of the conformal transformation between the Jordan and Einstein frames, not all the solutions in the Jordan frame are completely contained in the Einstein frame. We also make comparisons with previous dynamical systems approaches to f (R) cosmology and discuss their advantages and disadvantages.

Place, publisher, year, edition, pages
Institute of Physics Publishing (IOPP), 2016. no 8, 064
Keyword [en]
dark energy theory, inflation, modified gravity
National Category
Physical Sciences
Research subject
Physics
Identifiers
URN: urn:nbn:se:kau:diva-62616DOI: 10.1088/1475-7516/2016/08/064ISI: 000389859100002OAI: oai:DiVA.org:kau-62616DiVA: diva2:1130667
Available from: 2017-08-10 Created: 2017-08-10 Last updated: 2017-08-10Bibliographically approved

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Alho, ArturUggla, Claes
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  • apa
  • harvard1
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  • de-DE
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