Algebraic Observational Cosmology

TL;DR

This paper constructs an algebra of observables for a comoving observer in inflationary FLRW spacetimes, revealing how quantum degrees of freedom and horizon limitations influence entropy and measurement in cosmology.

Contribution

It introduces a framework for gravitationally-dressed observables in inflationary universes, highlighting the role of the inflaton zero-mode and horizon in entropy and state mixing.

Findings

Zero-mode fluctuations cause entropy in inflationary states.

All accessible states are mixed due to horizon inaccessibility.

Generalized entropy reflects initial conditions of the universe.

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.