Algebraic observational cosmology

What can be measured by an observer in a cosmological universe? We address this question by constructing an algebra of gravitationally dressed observables accessible to a comoving observer in Friedmann-Lemaître-Robertson-Walker spacetimes that are asymptotically de Sitter in the past, describing an inflationary epoch. The key feature of this model, compared to previous work, is that it captures the time dependence of an expanding cosmology. 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. Because of 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.