Turning big bang into big bounce. I. Classical dynamics

Abstract

The big bounce (BB) transition within a flat Friedmann-Robertson-Walker model is analyzed in the setting of loop geometry underlying the loop cosmology. We solve the constraint of the theory at the classical level to identify physical phase space and find the Lie algebra of the Dirac observables. We express energy density of matter and geometrical functions in terms of the observables. It is the modification of classical theory by the loop geometry that is responsible for BB. The classical energy scale specific to BB depends on a parameter that should be fixed either by cosmological data or determined theoretically at quantum level, otherwise the energy scale stays unknown.

Inflation in loop quantum cosmology: Dynamics and spectrum of gravitational waves

“…However, this expression is based on the computation of the area gap as performed in LQG. This, in general, can be questioned [12]. In particular, in the framework of reduced phase space quantization of LQC, the value of ρ c remains a free parameter [13].…”

Effective dynamics of the closed loop quantum cosmology

“…In this scheme new types of finite scale factor singularities appears. Another possibility is those presented in [14,15] whereμ = λ/ √ p and λ is some unknown constant unrelated with ∆.…”

“…However we do not apply this approach in our considerations. Recently also new approach to quantise loop quantum cosmological models has been proposed [14,15]. This formulation leads to the bouncing solutions but no effects of so called Thiemann's term, which leads to inverse volume corrections, are present.…”

Quantum theory of the Bianchi II model

“…Our investigations of the quantum Bianchi I model, based on a modification of the latter method, can be found in [11][12][13]. The goal of the present article is quite different.…”