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• W2892882322 abstract "It is a central goal of theoretical high-energy physics to develop a unifiedtheoretical framework that describes Nature on all scales. A common approachto this involves merging quantum theory and General Relativity into a unifiedtheory of quantum gravity. A theory of this kind has the potential to putcosmology on firm theoretical footing.String theory is a promising candidate for a unified theory. The second stringtheory revolution in the ’90s has consolidated the role of holography in quantumgravity in the form of a duality between quantum gravity with anti-de Sitter(AdS) boundary conditions and Conformal Field Theories (CFTs) defined on theconformal boundary of AdS. However observations indicate that our universe isasymptotically de Sitter (dS). Together these developments mean it is importantto understand whether holographic ideas can be developed and used in a dScontext to construct a quantum gravitational model of cosmology.A central role in quantum cosmology is played by the wave function of theuniverse. There are several indications indeed that the application of holographyto cosmology enables a new formulation of the wave function of the universe interms of the partition function of Euclidean deformed CFTs defined on the futureconformal boundary. However many fundamental questions about the technicaland conceptual nature of holographic cosmology or dS/CFT remain open. Inthis thesis we study and explore a number of features of dS/CFT duality. Inone particular example, AdS/CFT implies an explicit realization of dS/CFT,which relates Vasiliev’s higher spin theory of gravity to theO(N)vector modelof interacting scalars. This example will serve throughout this thesis as a usefultoy model with which we will explore and test various developments of theduality more generally.In the first part of this thesis we develop dS/CFT for Vilenkin’s tunnelingwave function and contrast its behaviour with that of the Hartle-Hawking wavefunction. We evaluate the holographic tunneling wave function in theO(N)vector toy model in the presence of a mass deformation and compare this withits behaviour predicted in the usual bulk saddle pont approximation.In the second part of this thesis we explore the dS/CFT correspondence withS1×S2future boundary conditions. In this context it has been argued that theprobability measure is badly defined, both in theO(N)vector toy model and inEinstein gravity, in the limit where the radius of theS1goes to zero. We analyzethis using quantum cosmology techniques to elucidate the interpretation of thewave function in this domain. We show that the divergent behaviour of the(bulk and boundary) measures occurs in a regime where the wave function doesnot describe asymptotically classical, Lorentzian histories and hence admitsno clean probabilistic interpretation. We also exhibit the strikingly differentbehaviour of the tunneling and no-boundary wave function in this regime. Theformer appears to select this quantum realm whereas the latter predicts theuniverse is everywhere in the semiclassical domain.The third part of this thesis consists of a digression into AdS/CFT. In the bulkwe consider a consistent truncation of M-Theory compactified onAdS4×S7consisting of Einstein gravity minimally coupled to a single scalar field with anegative exponential potential. We numerically find a three parameter familyof new Euclidean solutions of this theory that asymptote to a locally AdS spacewith a (double) squashed sphere as conformal boundary configuration. Oursolutions are generalization of the AdS Taub-NUT/Bolt solutions to include asecond squashing and scalar matter. We study their thermodynamic behaviouras a function of the three boundary parameters and show this qualitativelyreproduces that of the freeO(N)vector model defined on a double squashedsphere and deformed by a mass term.This sets the scene for the final part of this thesis where we consider complexgeneralizations of the above solutions, starting from the same theory, withasymptotically dS boundary conditions. These specify the saddle point wavefunction in a minisuperspace model of anisotropic deformations of dS with scalarmatter driving a regime of eternal inflation. We initiate a holographic explorationof eternal inflation by computing the partition function of the interactingO(N)vector model as a function of the three asymptotic parameters. We find that theamplitude is low for conformal boundary surfaces far from the round conformalstructure. This is in line with general field theory expectations and lendssupport to the conjecture that the exit from eternal inflation is reasonablysmooth, producing universes that are relatively regular on the largest scaleswith globally finite surfaces of constant density." @default.
• W2892882322 created "2018-10-05" @default.
• W2892882322 creator A5077723030 @default.
• W2892882322 date "2017-11-01" @default.
• W2892882322 modified "2023-09-24" @default.
• W2892882322 title "Holographic Wave Functions of the Universe" @default.
• W2892882322 hasPublicationYear "2017" @default.
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