Analysis of observables in FLRW spacetime

TL;DR

This paper models the cosmological fluid in a positively curved FLRW universe using quantum eigenstates of a Schrödinger equation, analyzing observables like the cosmological constant and gravitational entropy.

Contribution

It introduces a novel quantum mechanical framework for analyzing cosmological observables in FLRW spacetime, linking quantum states to cosmological parameters.

Findings

Complete set of quantum eigenstates derived

Matrix elements of cosmological constant computed

Gravitational entropy evaluated for quantum states

Abstract

We consider a positively curved FLRW spacetime as a background in which a nonrelativistic quantum particle propagates according to the Schroedinger equation. The probability fluid for the corresponding quantum states is taken as a model for the cosmological fluid filling this FLRW Universe. The Hamiltonian operator governing this fictitious particle is proportional to the Laplacian operator derived from the FLRW metric, while the mass of the particle equals the overall matter of the Universe (baryonic and dark). A complete, orthonormal set of quantum eigenstates of the Hamiltonian is obtained. Restricting to radially symmetric states, the latter are then used to compute matrix elements and expectation values of two observables for which quantum operators are identified, namely, the cosmological constant and the gravitational Boltzmann entropy. This entropy is regarded as corresponding to a positively-curved FLRW geometry when the cosmological fluid filling the Universe occupies a given quantum state.