In this paper we study quantum dynamics of the bouncing cosmological model. We focus on the model of the flat Friedmann-Robertson-Walker universe with a free scalar field. The bouncing behavior, which replaces the classical singularity, appears due to the modification of general relativity using the methods of loop quantum cosmology. We show that there exists a unitary transformation that enables one to describe the system as a free particle with a Hamiltonian equal to the canonical momentum. We examine properties of the various quantum states of the universe: the boxcar state, the standard coherent state, and the soliton-like state, as well as Schr\"odinger's cat states constructed from these states. Characteristics of the states---such as quantum moments and Wigner functions---are investigated. We show that each of these states have, for some range of parameters, a proper semiclassical limit fulfilling the correspondence principle. The decoherence of the superposition of two universes is described and possible interpretations in terms of triad orientation and the Belinsky-Khalatnikov-Lifshitz conjecture are given. We also examine negative-part sectors of the Wigner functions for the considered states. Their respective areas and localizations in the phase space feature an adequate estimate of nonclassicality. In particular, we show that regions where the Wigner function for the Glauber coherent cat state assumes its negative values have area equal to one fourth of the Planck constant. Based on the examined examples, we also conjecture that regions with negative values for the Wigner function are never smaller than one fourth of the Planck constant for states satisfying the uncertainty principle.
In this paper we study quantum dynamics of the bouncing cosmological model. We focus on the model of the flat Friedmann-Robertson-Walker universe with a free scalar field. The bouncing behavior, which replaces the classical singularity, appears due to the modification of general relativity using the methods of loop quantum cosmology. We show that there exists a unitary transformation that enables one to describe the system as a free particle with a Hamiltonian equal to the canonical momentum. We examine properties of the various quantum states of the universe: the boxcar state, the standard coherent state, and the soliton-like state, as well as Schr"odinger's cat states constructed from these states. Characteristics of the states---such as quantum moments and Wigner functions---are investigated. We show that each of these states have, for some range of parameters, a proper semiclassical limit fulfilling the correspondence principle. The decoherence of the superposition of two universes is described and possible interpretations in terms of triad orientation and the Belinsky-Khalatnikov-Lifshitz conjecture are given. We also examine negative-part sectors of the Wigner functions for the considered states. Their respective areas and localizations in the phase space feature an adequate estimate of nonclassicality. In particular, we show that regions where the Wigner function for the Glauber coherent cat state assumes its negative values have area equal to one fourth of the Planck constant. Based on the examined examples, we also conjecture that regions with negative values for the Wigner function are never smaller than one fourth of the Planck constant for states satisfying the uncertainty principle.
The quantum cosmology of the flat Friedmann-Lema\^{\i}tre-Robertson-Walker universe, filled with a scalar field, is considered in the de Broglie--Bohm (dBB) interpretation framework. A stiff-matter quantum bounce solution is obtained. The bouncing and subsequent pre-inflationary and inflationary dynamics are studied in details. We consider some representative primordial inflation models as examples, for which analytical expressions characterizing the dynamical quantities can be explicitly derived. The dependence of the inflationary dynamics on the quantum bounce parameters is then analyzed. The parameters emerging from our description are constrained by requiring the produced dynamics to be in accordance with some key cosmological quantities. The constraining conditions are also illustrated through regions of parameter space in terms of the bounce quantities.
We give an explicit, rigorous framework for calculating quantum probabilities in a model theory of quantum gravity. Specifically, we construct the decoherence functional for the Wheeler-DeWitt quantization of a flat Friedmann-Robertson-Walker cosmology with a free, massless, minimally coupled scalar field, thus providing a complete decoherent histories formulation for this quantum cosmological model. The decoherence functional is applied to study predictions concerning the model's Dirac (relational) observables; the behavior of semiclassical states and superpositions of such states; and to study the singular behavior of quantum Wheeler-DeWitt universes. Within this framework, rigorous formulas are given for calculating the corresponding probabilities from the wave function when those probabilities may be consistently defined, thus replacing earlier heuristics for interpreting the wave function of the universe with explicit constructions. It is shown according to a rigorously formulated standard, and in a quantum-mechanically consistent way, that in this quantization these models are generically singular. Independent of the choice of state we show that the probability for these Wheeler-DeWitt quantum universes to ever encounter a singularity is unity. In addition, the relation between histories formulations of quantum theory and relational Dirac observables is clarified.
This note extends the frame-deficit dictionary into an exactly solvable loop quantum cosmology structure, studying how information deficits, records, and entropic bounds behave through a quantum cosmological bounce. The model realizes the solvable loop quantum cosmology dynamics of a massless scalar universe on a lattice, where contraction, a positive-volume bounce, and expansion form a single unitary relational evolution. The paper establishes four results. First, the bounce is exactly characterized: every wavepacket universe contracts, reaches a minimum positive volume, and re-expands, with the expected symmetric bounce behavior of the solvable loop quantum cosmology model. Second, information is preserved across the bounce: relational evolution remains unitary, the pre-bounce state is recoverable, and the frame deficit remains invariant before, during, and after the bounce. Third, a quantum superposition of universes with different bounce times is studied. Matter records decohere the question of when the bounce occurred, and the interference between different bounce histories decreases exactly according to the record overlap. Fourth, the deficit–classicality entropic bound remains valid throughout the entire bounce evolution. The result extends the frame-deficit framework from Wheeler–DeWitt quantum cosmology to a nonsingular bouncing universe, showing that the information structure survives the transition replacing the classical singularity. The paper also distinguishes established loop quantum cosmology results from the new contribution: the bounce dynamics and cosmic recall belong to the existing solvable LQC framework, while the new results concern the information dictionary, the invariant deficit structure, and the exact bounce-time decoherence law. The scope is limited to the exactly solvable isotropic lattice realization of loop quantum cosmology. No claim is made for full Einstein dynamics, anisotropic models, or a complete theory of quantum gravity. All results are based on pre-registered predictions, computational verification, and reproducibility materials.
After a brief summary of the four main veins in the treatment of decoherence and quantum to classical transition in cosmology since the 1980s, we focus on one of these veins in the study of quantum decoherence of cosmological perturbations in inflationary universe, the case when it does not rely on any environment. This is what ‘intrinsic’ in the title refers to—a closed quantum system, consisting of a quantum field which drives inflation. The question is whether its quantum perturbations, which interact with the density contrast giving rise to structures in the universe, decohere with an inflationary expansion of the universe. A dominant view which had propagated for a quarter of a century asserts yes, based on the belief that the large squeezing of a quantum state after a duration of inflation renders the system effectively classical. This paper debunks this view by identifying the technical fault-lines in its derivations and revealing the pitfalls in its arguments which drew earlier authors to this wrong conclusion. We use a few simple quantum mechanical models to expound where the fallacy originated: The highly squeezed ellipse quadrature in phase space cannot be simplified to a line, and the Wigner function cannot be replaced by a delta function. These measures amount to taking only the leading order in the relevant parameters in seeking the semiclassical limit and ignoring the subdominant contributions where quantum features reside. Doing so violates the bounds of the Wigner function, and its wave functions possess negative eigenvalues. Moreover, the Robertson-Schrödinger uncertainty relation for a pure state is violated. For inflationary cosmological perturbations, in addition to these features, entanglement exists between the created pairs. This uniquely quantum feature cannot be easily argued away. Indeed, it could be our best hope to retroduce the quantum nature of cosmological perturbations and the trace of an inflation field. All this points to the invariant fact that a closed quantum system, even when highly squeezed, evolves unitarily without loss of coherence; quantum cosmological perturbations do not decohere by themselves.
The Everett-type interpretations of quantum mechanics and quantum cosmology proposed independently by Hartle, Geroch, and Wada are discussed. They essentially involve regarding a strong peak in the wave function as a definite prediction. Wave functions in quantum cosmology are usually peaked about correlations between coordinates and momenta, and methods for identifying such correlations are introduced. The first method involves Wigner's function, a quantum-mechanical analogue of the classical phase-space distribution. The properties of this distribution are discussed and it is shown how it can be of use in describing the emergence of classical behavior from quantum systems. The second method involves a suitably chosen canonical transformation. These methods are applied to harmonic-oscillator examples, which are of relevance to scalar field fluctuations in inflationary universe models. These methods are also applied to WKB wave functions in quantum mechanics and quantum cosmology. The manner in which the wave function becomes peaked about sets of classical solutions is elucidated. This is extended to include inhomogeneous perturbations about minisuperspace in quantum cosmology, and the derivation of the semiclassical Einstein equations, ${G}_{\ensuremath{\mu}\ensuremath{\nu}}$=8\ensuremath{\pi}G〈${T}_{\ensuremath{\mu}\ensuremath{\nu}}$〉, from the Wheeler-DeWitt equation is considered. A condition under which they are valid is derived. It is essentially the requirement that the distribution of ${T}_{\ensuremath{\mu}\ensuremath{\nu}}$, as a function of the matter modes, is strongly peaked about its average value. Some situations in which this condition is satisfied are discussed.