Author:

Keywords:

Quantum Cosmology, Holography

Abstract:

The goal of quantum cosmology is to find a quantum state that describes the entire evolution of our universe: from the fuzzy quantum dynamics dominating the universe’s evolution at early times to the classical cosmological evolution in our spacetime neighbourhood. Classical cosmology emerges in quantum cosmology under certain conditions only. In recent years significant progress has been made to understand the “classical realm” predicted by the No-Boundary Wave Function (NBWF), which will be the main focus of this thesis. However, it has not been understood how to go beyond this and learn something about the quantum realm of the universe as predicted by the NBWF. In this thesis we take a number of steps in this direction. The NBWF relates on a semiclassical level, Lorentzian de Sitter (dS) solutions to Euclidean Anti-de Sitter (AdS) solutions, which in their turn correspond, using the AdS/CFT conjecture, to a dual field theory defined on their boundary. This allows for a holographic formulation of the NBWF in which the relative weighting of different cosmological histories is given by the partition functions of (Euclidean) AdS/CFT duals. In this thesis we develop this novel holographic form of the NBWF in several directions. In the first part of this thesis we investigate the emergence of classical cosmological evolution from the boundary field theory and derive a sufficient set of conditions to obtain classical, Lorentzian bulk evolution at large spatial volumes. This derivation is based on the construction of a new wave function in terms of asymptotic variables, which are related to the sources of the dual field theory. With this new wave function it is possible to define new classicality conditions using the vacuum expectation values (vevs) from the dual boundary theory. In the second part of this thesis we look at the physics of eternal inflation, a regime where the dynamics of the theory is governed by large quantum fluctuations that get produced together with their backreaction on the geometry, meaning that the background does not evolve classically any more and that we therefore cannot get information about the global structure of the universe using the available techniques of the NBWF. With the use of the holographic NBWF proposal, it is possible to have an alternative calculation of the no-boundary measure, which is not plagued by the absence of a classical background. We show that it is possible to deduce some properties of the global structure of eternal inflation, by considering as a toy model a field theory living on a double squashed three-sphere. Both the squashed spheres and eternal inflation have highly curved regions and a high overall anisotropy. We start by calculating Euclidean AdS solutions that have the boundary of a squashed sphere and compare these with the free O(N) model. We find that the free energies of the two theories are remarkably similar, if we do not consider scalar excitations. We also comment on a universal property for CFTs on a squashed sphere. Namely, the field theory free energy has a local maximum in terms of the squashing parameter at zero squashing. Properties like this can be translated, using the holographic no-boundary conjecture, to cosmological spaces, with the result that the measure is peaked around isotropic universes, suggesting that holography predicts a smooth exit from eternal inflation. This is verified by the explicit calculation of the interacting O(N) model on the squashed sphere, which gives a distribution function that is globally peaked at the round sphere with zero scalar deformation with a low amplitude for geometries with negative scalar curvature. In the last part of this thesis we track the classical histories predicted by the NBWF back in time to the moment that the classicality conditions are not satisfied any more. Here, quantum-mechanical effects should be taken into account, making it possible that a classically forbidden transition happens between classical patches of cosmological evolution. We study these transitions by constructing complex saddle points that connect two classically evolving regions. The probabilities for transitions are then found to be the actions of these saddle points. We observe that universes at large values of the potential prefer a symmetric transition, while universes with a small value for the potential have a higher likelihood to transition to universes with a larger value of the potential.