Algebraic Observational Cosmology
Jun 3, 2024
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Abstract: (arXiv)
What can be measured by an observer in our universe? We address this question by constructing an algebra of gravitationally-dressed observables accessible to a comoving observer in FLRW spacetimes that are asymptotically de Sitter in the past, describing an inflationary epoch. An essential quantized degree of freedom is the zero-mode of the inflaton, which leads to fluctuations in the effective cosmological constant during inflation and prevents the existence of a maximum entropy state in the semiclassical limit. Due to the inaccessibility of measurements beyond our cosmological horizon, we demonstrate that all states are mixed with well-defined von Neumann entropy (up to a state-independent constant). For semiclassical states, the von Neumann entropy corresponds to the generalized entropy of the observer's causal diamond, a fine-grained quantity that is sensitive to the initial conditions of the universe.Note:
- 5 pages, 2 figures. v2: minor clarifications, references added
- entropy: von Neumann
- space-time: Robertson-Walker
- semiclassical
- inflation
- diamond
- causality
- zero mode
- algebra
- inflaton
- fluctuation
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Figures(3)
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