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On holographic methods in cosmology
On holographic methods in cosmology
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 space-time (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 non-trivial 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 Anti-de 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 space-times. 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.
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Heckelbacher, Till
2022
English
Universitätsbibliothek der Ludwig-Maximilians-Universität München
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 space-time (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 non-trivial 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 Anti-de 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 space-times. 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.