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Global dynamics and inflationary center manifold and slow-roll approximants
Technical University of Lisbon, Portugal.
Karlstad University, Faculty of Technology and Science. (Fysik)ORCID iD: 0000-0002-0906-8808
2015 (English)In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 56, no 1, 012502- p.Article in journal (Refereed) Published
Abstract [en]

We consider the familiar problem of a minimally coupled scalar field with quadratic potential in flat Friedmann-Lemaître-Robertson-Walker cosmology to illustrate a number of techniques and tools, which can be applied to a wide range of scalar field potentials and problems in, e.g., modified gravity. We present a global and regular dynamical systems description that yields a global understanding of the solution space, including asymptotic features. We introduce dynamical systems techniques such as center manifold expansions and use Padé approximants to obtain improved approximations for the “attractor solution” at early times. We also show that future asymptotic behavior is associated with a limit cycle, which shows that manifest self-similarity is asymptotically broken toward the future and gives approximate expressions for this behavior. We then combine these results to obtain global approximations for the attractor solution, which, e.g., might be used in the context of global measures. In addition, we elucidate the connection between slow-roll based approximations and the attractor solution, and compare these approximations with the center manifold based approximants.

Place, publisher, year, edition, pages
2015. Vol. 56, no 1, 012502- p.
Keyword [en]
Cosmology, scalar fields, attractors
National Category
Natural Sciences Physical Sciences
Research subject
URN: urn:nbn:se:kau:diva-35243DOI: 10.1063/1.4906081OAI: diva2:789308
Available from: 2015-02-18 Created: 2015-02-18 Last updated: 2015-07-06Bibliographically approved

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Uggla, Claes
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