Algebraic Observational Cosmology

Abstract

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.

Figures (3)

• Figure 1: The Penrose diagram for FLRW spacetimes that model our universe seeded from inflation. $\mathscr{D}$ is the domain of dependence for the observer $\gamma$, $\mathcal{H}^{+}$ is the future horizon of $\gamma$, $\mathcal{H}^{-}_{\textrm{R}}$ is the past horizon, and $\Sigma$ is a Cauchy surface for $\mathscr{D}$.
• Figure 2: Sketch of an inflaton potential with slow roll region (shaded in grey).
• Figure 3: An example of a globally hyperbolic extension $\overline{M}$ of the spacetime $M$ considered in this paper such that $\overline{M}$ is geodesically complete. This can be achieved by gluing the de Sitter region $\mathscr{D}' \cup \mathscr{P}$ to $M=\mathcal{F}\cup \mathscr{D}$.