{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,12]],"date-time":"2026-02-12T12:52:14Z","timestamp":1770900734147,"version":"3.50.1"},"reference-count":38,"publisher":"AIP Publishing","issue":"1","funder":[{"name":"Fundacao Ciencia e Tecnologia","award":["SFRH\/BPD\/85194\/2012"],"award-info":[{"award-number":["SFRH\/BPD\/85194\/2012"]}]}],"content-domain":{"domain":["pubs.aip.org"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2015,1,1]]},"abstract":"<jats:p>We consider the familiar problem of a minimally coupled scalar field with quadratic potential in flat Friedmann-Lema\u00eetre-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 Pad\u00e9 approximants to obtain improved approximations for the \u201cattractor solution\u201d 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.<\/jats:p>","DOI":"10.1063\/1.4906081","type":"journal-article","created":{"date-parts":[[2015,1,21]],"date-time":"2015-01-21T19:51:26Z","timestamp":1421869886000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":42,"title":["Global dynamics and inflationary center manifold and slow-roll approximants"],"prefix":"10.1063","volume":"56","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5753-8333","authenticated-orcid":false,"given":"Artur","family":"Alho","sequence":"first","affiliation":[{"name":"Center for Mathematical Analysis, Geometry and Dynamical Systems, Technical University of Lisbon 1 , 1049-001 Lisbon, Portugal"}]},{"given":"Claes","family":"Uggla","sequence":"additional","affiliation":[{"name":"University of Karlstad 2 Department of Physics, , S-651 88 Karlstad, Sweden"}]}],"member":"317","published-online":{"date-parts":[[2015,1,21]]},"reference":[{"key":"2023080400165821900_c1","doi-asserted-by":"publisher","first-page":"241101","DOI":"10.1103\/PhysRevLett.112.241101","article-title":"Detection of B-mode polarization at degree angular scales by BICEP2","volume":"112","author":"BICEP2 Collaboration","year":"2014","journal-title":"Phys. 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