Narrow Results

Using the right representation in the evaluation of the creation probability of the universe, one can show that the external dimension of the Freund–Rubin model is min(s,n-s), where s is the rank of the antisymmetric field strength in the model.

We show how, in canonical quantum cosmology, the frame fixing induces a new energy density contribution having features compatible with the (actual) cold dark matter component of the Universe. First we quantize the closed Friedmann–Robertson–Walker (FRW) model in a synchronous reference and determine the spectrum of the super-Hamiltonian in the presence of ultra-relativistic matter and a perfect gas contribution. Then we include in this model small inhomogeneous (spherical) perturbations in the spirit of the Lemaitre–Tolman cosmology. The main issue of our analysis consists in outlining that, in the classical limit, the nonzero eigenvalue of the super-Hamiltonian can account for the present value of the dark matter critical parameter. Furthermore we obtain a direct correlation between the inhomogeneities in our dark matter candidate and those that appear in the ultra-relativistic matter.

We present a brief summary of the developments of no-boundary quantum cosmology for the last three decades.

We propose a mechanism to have a smooth transition from a pre-Big Bang phase to a standard cosmological phase. Such transition is driven by gravitational production of heavy massive string states that backreact on the geometry to stop the growth of the curvature. Close to the string scale, particle creation can become effective because the string phase space compensate the exponential suppression of the particle production. Numerical solutions for the evolution of the Universe with this source are presented.

We review some aspects of quantum gravity in the context of cosmology. In particular, we focus on models with a phenomenology accessible to current and near-future observations, as the early Universe might be our only chance to peep through the quantum gravity realm.

This papers offers a critical discussion on the procedure by which Loop Quantum Cosmology (LQC) is constructed from the full Loop Quantum Gravity (LQG) theory. Revising recent issues in preserving SU(2) symmetry when quantizing the isotropic Universe, we trace a new perspective in approaching the cosmological problem within quantum geometry. The cosmological sector of LQG is reviewed and a critical point of view on LQC is presented. It is outlined how a polymer-like scale for quantum cosmology can be predicted from a proper fundamental graph underlying the homogeneous and isotropic continuous picture. However, such a minimum scale does not coincide with the choice made in LQC. Finally, the perspectives towards a consistent cosmological LQG model based on such a graph structure are discussed.

We present and expand the simplest possible quantum cosmological bouncing model already discussed in previous works: the trajectory formulation of quantum mechanics applied to cosmology (through the Wheeler–De Witt equation) in the Friedmann–Lemaître–Robertson–Walker (FLRW) minisuperspace without spatial curvature. The initial conditions that were previously assumed were such that the wave function would not change its functional form but instead provide a dynamics to its parameters. Here, we consider a more general situation, in practice consisting of modified Gaussian wave functions, aiming at obtaining a nonsingular bounce from a contracting phase. Whereas previous works consistently obtain very symmetric bounces, we find that it is possible to produce highly non-symmetric solutions, and even cases for which multiple bounces naturally occur. We also introduce a means of treating the shear in this category of models by quantizing in the Bianchi I minisuperspace.

This work is devoted to the spatially open Friedmann–Robertson–Walker (FRW) Universe evolving from the stiff matter era to the dust dominated one. Within the quantum analysis based on the Wheeler–DeWitt equation, we derive the wave function of the $(k=-1)$-FRW Universe with combined matter sources. On the classical level, one has to deal with the Friedmann equation which leads on a dependence of the scale function on time generally expressed from functional relations involving elliptic integrals.

In this paper, we consider the De Broglie–Bohm interpretation of a Hořava–Lifshitz quantum cosmology model in the presence of a radiation perfect fluid. We compute the Bohm’s trajectory for the scale factor and show that it never goes to zero. That result gives a strong indication that this model is free from singularities at the quantum level. We also compute the quantum potential. That quantity helps in understanding why the scale factor never vanishes.

We consider quantization of the gravity-scalar field system in the minisuperspace approximation. It turns out that in the gauge fixed deparametrized theory where the scale factor plays the role of time, the Hamiltonian can be uniquely defined without any ordering ambiguity as the square root of a self-adjoint operator. Moreover, the Hamiltonian degenerates to zero and the Schrödinger equation becomes well behaved as the scale factor vanishes. Therefore, there is no technical or physical obstruction for the initial wave function of the universe to be an arbitrary vector in the Hilbert space, which demonstrates the severeness of the initial condition problem in quantum cosmology.

We start by presenting a brief summary of fractional quantum mechanics, as means to convey a motivation towards fractional quantum cosmology. Subsequently, such application is made concrete with the assistance of a case study. Specifically, we investigate and then discuss a model of stiff matter in a spatially flat homogeneous and isotropic universe. A new quantum cosmological solution, where fractional calculus implications are explicit, is presented and then contrasted with the corresponding standard quantum cosmology setting.

We have recently proposed a Lagrangian in trace dynamics to describe a possible unification of gravity, Yang–Mills fields, and fermions, at the Planck scale. This Lagrangian for the unified entity — called the aikyon — is invariant under global unitary transformations, and as a result possesses a novel conserved charge, known as the Adler–Millard charge. In this paper, we derive an eigenvalue equation, analogous to the time-independent Schrödinger equation, for the Hamiltonian of the theory. We show that in the emergent quantum theory, the energy eigenvalues of the aikyon are characterized in terms of a fundamental frequency times Planck’s constant. The eigenvalues of this equation can, in principle, determine the values of the parameters of the standard model. We also report a ground state, in this theory of spontaneous quantum gravity, which could characterize a non-singular initial epoch in quantum cosmology.

For the first time, we choose non-flat vacuum mode for background spacetime based on the minimum number of created particles during early non-de Sitter inflation. In conventional methods for calculating the number of created particles, the flat background is selected automatically and causes a negative number problem for created particles during asymptotic-de Sitter inflation. In a covariant approach to curved spacetime, both real and background spacetimes should be selected, curved and consequently the relation for particle creation should be modify. As an interesting finding from this research, flat space does not include minimum number of particles and there are some asymptotic de Sitter spacetimes with fewer number. Therefore, in the generalized formula for particle creation, we choose a non-flat background containing the minimum number of created particles.

It is well known that classical Unimodular Gravity (UG) is equivalent to General Relativity, but the equivalence at the quantum level is not clear. Here we exhibit, in the UG framework, the Quantum Cosmology (QC) for a Friedmann–Lemaitre–Robertson–Walker (FLRW) universe, considering an inflationary scenario and also introducing a deformation on the commutation relations for the minisuperspace variables (NCC).

In this paper, we have suggested that the late time expansion of the Universe is caused by the absorption of baby universes. This absorption leads to a modified Friedmann equation with one free parameter B replacing the cosmological constant. The late time cosmology is modified in such a way that one can obtain agreement with the measured values of the Hubble parameter H(z) for z between 0 and the value corresponding to the time of last scattering of CMB for a suitable choice of B. In this paper, we show that the modified Friedmann equation with this choice of B also describes well other aspects of the large-scale structure of the Universe.

In the background of homogeneous and isotropic flat FLRW spacetime, both classical and quantum cosmologies have been studied for teleparallel dark energy (DE) model. Using Noether symmetry analysis, not only the symmetry vector but also the coupling function in the Lagrangian and the potential of the scalar field have been determined. Also symmetry analysis identifies a cyclic variable in the Lagrangian along the symmetry vector and as a result the Lagrangian simplifies to a great extent so that classical solution is obtained. Subsequently, in quantum cosmology Wheeler–DeWitt (WD) equation has been constructed and the quantum version of the conserved momenta corresponding to Noether symmetry identifies the periodic part of the wave function of the universe and as a result the WD equation becomes solvable. Finally, quantum description shows finite nonzero probability at the classical big bang singularity.

In this paper, we apply quantum cosmology to investigate the early moments of a Friedmann–Lemaître–Robertson–Walker (FLRW) cosmological model, using Hořava–Lifshitz (HL) as the gravitational theory. The matter content of the model is a dust perfect fluid. We start studying the classical model. Then, we write the total Hamiltonian of the model, quantize it and find the appropriate Wheeler–DeWitt equation. In order to avoid factor ordering ambiguities, in the Wheeler–DeWitt equation, we introduce a canonical transformation. We solve that equation using the Wentzel–Kramers–Brillouin (WKB) approximation and compute the tunneling probabilities for the birth of that universe ($\text{T}{\text{P}}_{\mathrm{\text{WKB}}}$). Since the WKB wave function depends on the dust energy and the free coupling constants coming from the HL theory, we compute the behavior of ${\mathrm{\text{TP}}}_{\mathrm{\text{WKB}}}$ as a function of all these quantities.

The present work investigates the implications of incorporating noncommutativity into $f(R)$ gravity. In particular, we explore the proposed framework in a flat Friedmann–Robertson–Lamaître–Walker background. We introduced the noncommutativity between the coordinates and the momenta, in a $2n$-dimensional phase space. Applying the machinery of canonical quantization we obtain the noncommutative version of the Wheeler–DeWitt equation, and using a WKB-type approximation we can get analytical solutions for the model examining two cases for the leading noncommutative coefficient. In the first, solutions for the scale factor present a structure similar to previous solutions reported in the literature. The second one, in contrast to its commutative counterpart, the solutions obtained for the scale factor show that its evolution has the behavior of a non-singular cyclic universe. Also, we present the demeanor of the Hubble parameter and the effective equation of state parameter, where the latter crosses the “$-1$” divide line.

Previous analysis about the deparametrization and path integral quantization of cosmological models are extended to models which do not admit an intrinsic time. The formal expression for the transition amplitude is written down for the Taub anisotropic universe with a clear notion of time. The relation existing between the deparametrization associated to gauge fixation required in the path integral approach and the procedure of reduction of the Wheeler–DeWitt equation is also studied.

The rotation of astronomical objects may be of a cosmological origin due to the Universe's specific angular momentum estimates proving to exceed those for spiral galaxies. The problem is expected to be solved in the framework of quantum geometrodynamics.