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.
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.
In a previous work we have exhibited a clear description of the quantum-to-classical transition of cosmological quantum fluctuations in the inflationary scenario using the de Broglie--Bohm quantum theory. These fluctuations are believed to seed the small inhomogeneities, which are then responsible for the formation of large scale structures. In this work we show that using the de Broglie--Bohm theory, it is also possible to describe the quantum-to-classical transition of primordial perturbations which takes place around a bouncing phase, even if the latter is caused by quantum effects due to the quantization of the background geometry.
We review the de Broglie–Bohm quantum theory. It is an alternative description of quantum phenomena in accordance with all the quantum experiments already performed. Essentially, it is a dynamical theory about objectively real trajectories in the configuration space of the physical system under investigation. Hence, it is not necessarily probabilistic, and it dispenses with the collapse postulate, making it suitable to be applied to cosmology. The emerging cosmological models are usually free of singularities, with a bounce connecting a contracting era with an expanding phase, which we are now observing. A theory of cosmological perturbations can also be constructed under this framework, which can be successfully confronted with current observations, and can complement inflation or even be an alternative to it.
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.
Abstract In quantum cosmology, one has to select a specific wave function solution of the quantum state equations under consideration in order to obtain concrete results. The simplest choices have been already explored, in different frameworks, yielding, in many cases, quantum bounces. As there is no consensually established boundary condition proposal in quantum cosmology, we investigate the consequences of enlarging known sets of initial wave functions of the Universe, in the specific framework of the Wheeler–DeWitt equation interpreted along the lines of the de Broglie–Bohm quantum theory, on the possible quantum bounce solutions which emerge from them. In particular, we show that many asymmetric quantum bounces are obtained, which may incorporate non-trivial back-reaction mechanisms, as quantum particle production around the bounce, in the quantum background itself. In particular, the old hypothesis that our expanding Universe might have arisen from quantum fluctuations of a fundamental quantum flat space-time is recovered, within a different and yet unexplored perspective.
Abstract We investigate the dynamical stability and relaxation of subquantum non-equilibrium states within the framework of De Broglie Bohm field theory during primordial inflation. By evaluating the quantum Hamilton-Jacobi formalism on a covariant Friedmann-Lemaître Robertson-Walker (FLRW) background, I demonstrate that non-linearities intrinsic to the field-theoretic quantum potential generate microscopic phase-space chaos. I solve the Jacobi deviation equation for coupled Fourier modes and extract the maximal Lyapunov exponent spectrum. I find that sub-horizon modes exhibit rapid exponential trajectory divergence driving coarse-grained subquantum entropy toward zero via Valentini's subquantum H-theorem. This dynamic phase-mixing enforces the Born rule well before horizon crossing, rendering anti-relaxation statistically prohibited for generic inflationary potentials. Finally, I map residual non-equilibrium corrections onto the Cosmic Microwave Background (CMB) power spectrum at low multipoles establishing current observational bounds from Planck 2018 data and providing forecasts for B-mode polarization measurements from LiteBIRD and CMB-S4.
We construct a Bohmian quantum cosmological model for a spatially flat Friedmann-Robertson-Walker universe filled with a single scalar field whose potential provides a unified description of cold dark matter and dark energy at the background level. Starting from the Einstein-Hilbert action supplemented by a scalar field, we derive the minisuperspace Lagrangian and the associated canonical Hamiltonian formulation. By means of a nontrivial canonical transformation, the minisuperspace dynamics is mapped into that of a two-dimensional hyperbolic oscillator with a fixed frequency ratio, rendering the Wheeler-DeWitt equation exactly solvable by separation of variables. The resulting Wheeler-DeWitt solutions are expressed in terms of parabolic cylinder functions and are parametrised by a continuous separation constant, reflecting the constrained nature of the theory and the absence of a standard Schrödinger time parameter. Adopting the de Broglie-Bohm formulation, we derive deterministic guidance equations in minisuperspace and construct a well-defined Bohmian Hubble parameter directly in terms of the pilot-wave phase. Finally, we present a Wheeler-DeWitt-derived toy wave function for which the Bohmian trajectories and the associated cosmological expansion history can be obtained analytically, reproducing the late-time ΛCDM behaviour while exhibiting quantum modifications at earlier epochs.