Semiclassical States in Quantum Cosmology: Bianchi I Coherent States

TL;DR

This paper constructs and analyzes semiclassical coherent states for Bianchi I quantum cosmological models, exploring their properties in both kinematical and physical Hilbert spaces and examining their evolution over time.

Contribution

It provides a method to explicitly construct semiclassical states in quantum cosmology and analyzes their physical relevance and time evolution.

Findings

Good semiclassical physical states can be constructed via group averaging.

Kinematical states can approximate physical states under certain conditions.

Intrinsic coherent states spread over time, affecting their semiclassical validity.

Abstract

We study coherent states for Bianchi type I cosmological models, as examples of semiclassical states for time-reparametrization invariant systems. This simple model allows us to study explicitly the relationship between exact semiclassical states in the kinematical Hilbert space and corresponding ones in the physical Hilbert space, which we construct here using the group averaging technique. We find that it is possible to construct good semiclassical physical states by such a procedure in this model; we also discuss the sense in which the original kinematical states may be a good approximation to the physical ones, and the situations in which this is the case. In addition, these models can be deparametrized in a natural way, and we study the effect of time evolution on an "intrinsic" coherent state in the reduced phase space, in order to estimate the time for this state to spread significantly.