Applications of Curved Space Field Theory to Simple Scalar Field Models of Inflation

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http://urn.fi/URN:ISBN:978-952-10-8961-9
Title: Applications of Curved Space Field Theory to Simple Scalar Field Models of Inflation
Author: Markkanen, Tommi
Contributor: University of Helsinki, Faculty of Science, Department of Physics
Publisher: Helsingin yliopisto
Date: 2014-05-05
URI: http://urn.fi/URN:ISBN:978-952-10-8961-9
http://hdl.handle.net/10138/44865
Thesis level: Doctoral dissertation (article-based)
Abstract: Cosmic inflation is a phase of accelerating, nearly exponential expansion of the spacetime fabric of the Universe, which is assumed to have taken place almost immediately after the Big Bang. Inflation possesses the appealing property that it provides solutions to deep cosmological problems, such as the flatness and horizon problems, and also gives a natural origin for the formation of the large scale structures we observe today. In this thesis we set out to investigate the role quantum corrections play for some simple models where inflation is driven by a single scalar field. It is essential that here the quantum corrections are calculated via curved space field theory. In this technique one quantizes only the matter fields, the dynamics of which take place on a curved classical background. This approach is rarely used in mainstream cosmology and it has the benefit that it allows the quantum fluctuations to back-react on classical Einsteinian gravity. The curved space quantum corrections are studied first in the effective action formalism via the Schwinger-DeWitt expansion and then by constructing effective equations of motion by using the slow-roll technique. We also focus on consistent renormalization and show how to renormalize the effective equations of motion without any reference to an effective action for an interacting theory in curved spacetime. Due to a potential infrared enhancement in effective equations in quasi-de Sitter space, we also perform a resummation of Feynman diagrams in curved non-static space and observe that it regulates the infrared effects. Concerning implications for actual inflationary models, we focus on chaotic type models and observe the quantum corrections to be insignificant, but nevertheless to have theoretically a non-trivial structure.Kosmiseksi inflaatioksi kutsutaan maailmankaikkeuden syntyhetkiä seurannutta ajanjaksoa, jolloin aika-avaruuden uskotaan laajenneen kiihtyvällä nopeudella. Inflaatio tarjoaa selitykset akaisemmin ratkaisemattomiin syviin kosmologisiin ongelmiin, ehkä tärkeimpänä, syyn siihen miksi kosminen taustasäteily ei sisällä suuria lämpotilavaihteluita. Maailmankaikkeuden suuret rakenteet kuten galaksit ja tähdet ovat myös inflaation luonnollinen seuraus. Tämän väitöksen tarkoituksena on tutkia kvanttikorjausten merkitystä yksinkertaisiin inflaatiomalleihin. Kvanttikorjaukset on laskettu kaarevassa, joskin klassisessa aika-avaruudessa, mikä sallii kvanttiefektien vaikutuksen myös painovoiman käytökseen. Kvanttikorjauksien laskemiseen sovelletaan derivaattaekspansiota sekä hitaan vierimisen (slow-roll) approksimaatiota. Lisäksi liikeyhtälöiden renormalisoimiseksi johdetaan uusi konsistentti metodi. Ratkaisujen ongelmallinen infrapunakäytös regularisoidaan ei-perturbatiivisella ekspansiolla. Tuloksissa keskitytään kaoottisiin malleihin, joissa huomataan korjausten olevan pieniä, mutta teoreettisesti epätriviaaleja.
Subject: teoreettinen fysiikka
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