Gaussian state for the bouncing quantum cosmology

Abstract

We present results concerning propagation of the Gaussian state across the cosmological quantum bounce. The reduced phase space quantization of loop quantum cosmology is applied to the Friedman-Robertson-Walker universe with a free massless scalar field. Evolution of quantum moments of the canonical variables is investigated. The covariance turns out to be a monotonic function so it may be used as an evolution parameter having quantum origin. We show that for the Gaussian state the Universe is least quantum at the bounce. We propose explanation of this counter-intuitive feature using the entropy of squeezing. The obtained time dependence of entropy is in agreement with qualitative predictions based on von Neumann entropy for mixed states. We show that, for the considered Gaussian state, semiclassicality is preserved across the bounce, so there is no cosmic forgetfulness.Comment: 7 pages, 7 figures; matches version published in Phys. Rev.

A critical review of classical bouncing cosmologies

“…If one takes this framework as a working hypothesis, ignoring possible observational and theoretical shortcomings, it was shown that the initial singularity is resolved [87] and inflationary as well as bouncing cosmologies may be achieved [88][89][90][91][92][93][94][95][96][97][98] (see also [99] for a related approach involving a minimal length). A consistent treatment of perturbations in LQC has been proposed in Refs.…”

“…Several attempts have been made to incorporate fluctuations into the framework of a bouncing LQC setup ( [93,94] and references therein). It is possible to accommodate a scale-invariant spectrum if at least one scalar field and either a matter phase [106], or a second scalar field combined with an entropic mechanism, is introduced.…”

Bianchi IX model: Reducing phase space

“…The issue of an evolution of the quantum Bianchi IX model has not been considered so far, to such an extent as has been done for the Friedman-Robertson-Walker and the Bianchi I models within the reduced phase space quantization method (see, e.g., Refs. [12][13][14][15][16]). …”

“…It is clear that in the former case we get the true Hamiltonian that can be later used in describing the quantum evolution of the system. Having a physical Hamiltonian is the ''first things first'' of our quantization scheme [12][13][14][15][16]. In the latter case, an evolution of the system is defined, at the quantum level, by rewriting the constraint operator in the form leading to the Schrödinger-like equation (see, e.g., Ref.…”

“…However, what has been achieved so far is not satisfactory for us, as we wish to work out a classical formalism that would be suitable for the quantization method that we developed recently (see, e.g., Refs. [11][12][13][14][15][16]). …”