Heckelbacher, Till (2022): On holographic methods in cosmology. Dissertation, LMU München: Faculty of Physics 

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Abstract
In this thesis we consider cosmological correlation functions of a quantum field theory in the asymptotic future of a Universe with an accelerated expansion. In particular, we calculate quantum corrections to the four point function of a conformally coupled scalar field with a quartic interaction term up to one loop order in a four dimensional de Sitter spacetime (dS). This can be expanded in terms of conformal blocks of a dual theory and we determine the conformal data up to the second order in perturbation theory. We find closed expressions for all anomalous dimensions. Since they obey some nontrivial conformal consistency conditions, we show, up to first loop order, that cosmological correlation functions in the asymptotic future of dS are holographically determined by a euclidean, conformal field theory. In an intermediate step we calculate quantum corrections of the same theory in euclidean Antide Sitter space (EAdS) which we expand in terms of conformal blocks as well and find closed expressions for all anomalous dimensions. To perform these computations we develope a method to map the involved integrals to equivalent expressions in flat space, which we evaluate analytically, using established techniques from the calculation of Feynman integrals. For that, we construct an adapted dimensional regularisation scheme for curved spacetimes. We show that, up to the considered order, all conformal correlation functions can be expressed in terms of multiple polylogarithms while the integrals in EAdS contain elliptic polylogarithms as well.
Item Type:  Theses (Dissertation, LMU Munich) 

Subjects:  500 Natural sciences and mathematics 500 Natural sciences and mathematics > 530 Physics 
Faculties:  Faculty of Physics 
Language:  English 
Date of oral examination:  24. June 2022 
1. Referee:  Sachs, Ivo 
MD5 Checksum of the PDFfile:  bf9aaf1df3748d071e8b0195c1a7918b 
Signature of the printed copy:  0001/UMC 28902 
ID Code:  30174 
Deposited On:  11. Jul 2022 14:17 
Last Modified:  11. Jul 2022 14:17 