In this thesis, we investigate the thermodynamics of the de Sitter static patch in order to extract information which can constrain microscopic models of de Sitter quantum gravity.
We begin by reviewing previous works which demonstrate how to make sense of the seemingly ill-defined static patch density of states through the introduction of Harish-Chandra group characters, or equivalently through renormalization with respect to a reference problem in Rindler space. A thermal partition function can then be constructed and expressed in terms of a sum over quasinormal mode frequencies. We recap how, in the scalar case, this partition function is equivalent to a 1-loop sphere path integral, as expected from the Gibbons-Hawking proposal, and provides macroscopic data which microscopic models must be consistent with.
We next present novel results dealing with scalar Green functions in de Sitter. After constructing various static patch correlators and showing how they can be obtained from their sphere counterparts, we relate the spectral Green function to the Harish-Chandra characters that we came across before, tying them to observables directly accessible within the static patch. We comment on how this result will allow us to generalize thermodynamic considerations to interacting theoriesand therefore place stronger consistency constraints on microscopic models.
We finally generalize our analysis to spinning fields, for which thermal partition functions differ from Euclidean path integrals by edge corrections. We reveal new findings which trace the source of these discrepancies to those quasinormal modes which do not correspond to regular Euclidean solutions, explicitly demonstrating this through several examples. Our results highlight the differences between Lorentzian and Euclidean approaches to de Sitter thermodynamics, and hint at new avenues to pursue in the hopes of providing more consistency constraints.
| Identifer | oai:union.ndltd.org:columbia.edu/oai:academiccommons.columbia.edu:10.7916/djnq-y976 |
| Date | January 2024 |
| Creators | Grewal, Manvir |
| Source Sets | Columbia University |
| Language | English |
| Detected Language | English |
| Type | Theses |
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