Coherent semiclassical states for loop quantum cosmology

TL;DR

This paper constructs and analyzes coherent semiclassical states in loop quantum cosmology, demonstrating their stability through the bounce and showing Gaussian states are more reliable than squeezed states for preserving semiclassicality.

Contribution

It introduces a family of exact coherent states in loop quantum cosmology and evaluates their semiclassical properties near the bounce, confirming the robustness of Gaussian states.

Findings

States remain sharply peaked and semiclassical at the bounce.

Effective theory accurately describes the dynamics throughout evolution.

Gaussian states exhibit better semiclassical behavior than squeezed states.

Abstract

The spatially flat Friedman-Robertson-Walker (FRW) cosmological model with a massless scalar field in loop quantum cosmology admits a description in terms of a completely solvable model. This has been used to prove that: i) the quantum bounce that replaces the big bang singularity is generic; ii) there is an upper bound on the energy density for all states and iii) semiclassical states at late times had to be semiclassical before the bounce. Here we consider a family of exact solutions to the theory, corresponding to generalized coherent Gaussian and squeezed states. We analyze the behavior of basic physical observables and impose restrictions on the states based on physical considerations. These turn out to be enough to select, from all the generalized coherent states, those that behave semiclassical at late times. We study then the properties of such states near the bounce where the most `quantum behavior' is expected. As it turns out, the states remain sharply peaked and semiclassical at the bounce and the dynamics is very well approximated by the `effective theory' throughout the time evolution. We compare the semiclassicality properties of squeezed states to those of the Gaussian semiclassical states and conclude that the Gaussians are better behaved. In particular, the asymmetry in the relative fluctuations before and after the bounce are negligible, thus ruling out claims of so called `cosmic forgetfulness'.