On the Physical Hilbert Space of Loop Quantum Cosmology

TL;DR

This paper constructs and analyzes the physical Hilbert space in Riemannian and Lorentzian loop quantum cosmology, revealing that with a cosmological constant, the space is separable with a single state, impacting standard models.

Contribution

It provides an explicit construction of the physical Hilbert space in loop quantum cosmology with a cosmological constant, including exact solutions and implications for Lorentzian models.

Findings

Physical Hilbert space is separable with a single state when matter includes a cosmological constant.

Explicit construction of the physical Hilbert space using refined algebraic quantization.

Extension of the model to Lorentzian sector with significant implications.

Abstract

In this paper we present a model of Riemannian loop quantum cosmology with a self-adjoint quantum scalar constraint. The physical Hilbert space is constructed using refined algebraic quantization. When matter is included in the form of a cosmological constant, the model is exactly solvable and we show explicitly that the physical Hilbert space is separable consisting of a single physical state. We extend the model to the Lorentzian sector and discuss important implications for standard loop quantum cosmology.