UBC Theses and Dissertations
Towards a holographic universe Sahu, Abhisek
In this thesis, we present a bottom-up holographic model for a large class of time- reversal symmetric cosmological spacetimes, through the anti-de Sitter/conformal field theory (AdS/CFT) correspondence. A major challenge in describing cosmological spacetimes using the AdS/CFT correspondence, is that they often do not have an anti-de Sitter (AdS) boundary. To solve this problem we have constructed a geometry by embedding spherically symmetric regions of a Friedmann-Lemaître-Robertson-Walker (FLRW) spacetime with a given scale factor inside a Schwarzschild-AdS (SAdS) spacetime, with the simple assumption that the two regions are separated by a thin shell satisfying Israel junction conditions. To ensure there exists a quantum state in the conformal field theory (CFT) which is dual to the bulk spacetime, we consider only time-reversal symmetric bubble spacetimes. This property allows us to define a real Euclidean spacetime by analytically continuing to imaginary times. We show that in certain cases, the Euclidean spacetime with its non-trivial asymptotic structure in form of the combined Euclidean AdS boundary of the FLRW cosmology and the SAdS boundary, gives rise to a natural state of the CFT via a Euclidean path integral. We also demonstrate the embedding procedure and existence of non-trivial asymptotics through some explicit examples. At this point two significant complications may arise. Firstly, to have the Euclidean asymptotics and time-reversal symmetry discussed above, we need cosmologies with a fundamentally negative cosmological constant, Λ. We argue that although the Λ-cold dark matter (ΛCDM) model points towards a small positive Λ, there is a plausible path forward with a model with a time dependent scalar field with a potential that is currently positive, but rolling towards a negative value to give us an effective negative Λ. Secondly, it is possible that our bubble lies behind the horizon of the SAdS black hole where we typically can’t probe. This problem is solved by a thorough analysis of the model’s parameter space, which suggests there is always a large set of parameters allowing embedding arbitrarily large bubbles of cosmology that peek out of the horizon.
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