Quantum graviton creation in a model universe

Quantization in the spatially inhomogeneous, anisotropic, Gowdy three-torus solution of Einstein's equations leads to the production of gravitons from empty space. The creation of pairs of gravitons occurs only in wave modes with wavelength exceeding the horizon size at an initial time. The final number of created gravitons in any mode is proportional to the number of causally unconnected regions at the initial time over the wavelength of that mode. At large times, graviton number is well defined since the solution is in WKB form. The creation process produces the anisotropic collisionless radiation identical to that discussed by Doroshkevich, Zel'dovich, and Novikov which characterizes the large time classical solution. Near the singularity, the model behaves like an empty Bianchi Type I universe at each point in space (local Kasner). The canonical methods of Arnowitt, Deser, and Misner yield a reduced Hamiltonian from which the classical equations of motion are obtained. The quantization of the rapidly varying gravitational field component resembles the procedures used by Parker or Zel'dovich et al. to study particle creation in curved spacetime.     

Quantum creation of the universe with a minimum scalar-field energy

The quantum creation of a closed Friedmann universe is studied on the basis of a Wheeler-DeWitt equation with two arguments — a scale factor and a scalar-field potential. In the quasiclassical approximation the wave function of the universe (WF) starts to evolve at a zero scalar field. A near-Planckian energy density of the field arises as a result of tunneling through a potential barrier. In our opinion, this variant of the scenario most closely resembles creation ex nihilo. The only parameter controlling quantum evolution is the mass of a quantum of the scalar field. In the paper by Khalatnikov and Schiller [JETP Lett. 57,1 (1993)], tunneling through the classically inaccessible region of the superpotential U(a,φ) is calculated by the instanton method. However, this method requires that the potential U(a,φ) satisfy special conditions in the space (a,φ). For this reason, in the present paper the tunneling calculation is performed by the method of characteristics for the quasiclassical approximation of the Wheeler-DeWitt equation under the barrier. The WKB theory, which has been well-developed for one-dimensional problems, is employed along each characteristic. It is shown that the corresponding turning points are also points where U(a, φ)=0. The total barrier penetrability is obtained by averaging over a bundle of characteristics. Pis’ma Zh. éksp. Teor. Fiz. 64, No. 5, 305–308 (10 September 1996)     

Particle creation in a cosmological anisotropic universe

We analyze the phenomenon of particle creation in a cosmological anisotropic universe. We compute, via the Bogoliubov transformations, the density number of scalar and spin-1/2 particles created. We obtain that they are respectively described by Bose-Einstein and Fermi-Dirac distributions.     

The creation of the universe as a quantum phenomenon

Quantum creation of massy particles can occur in the cosmological context without cost of energy. This fact is seized upon to construct a causal open homogeneous isotropic cosmology. The universe is conceived as the response of matter and the gravitational field to a spontaneous pointlike disturbance. Its history unfolds in two stages, creation and free expansion. The first stage gives rise to a “fireball.” The free expansion is extrapolated back to the “fireball.” The latter thus replaces the “big-bang,” thereby avoiding an initial singularity. Though not intrinsic to the theory it does suggest the interpretation of the cosmological part of the gravitational field as the scalar dilaton that is encountered in the dynamical generation of mass in conformally invariant theory.     

The creation of particles from a vacuum in a nonsteady isotropic universe

The paper considers the creation of particles from a vacuum in a closed, open, and quasi-Euclidean Friedmann model. Finite general expressions are obtained for the density of the number of pairs created, and also new analytical estimates are given of the intensity of processes of creation at different stages of evolution of the universe.     

Quantum cosmology of the brane universe

We canonically quantize the dynamics of the brane universe embedded into the five-dimensional Schwarzschild-anti-de Sitter bulk space-time. We show that in the brane-world settings the formulation of the quantum cosmology, including the problem of initial conditions, is conceptually more simple than in the (3+1)-dimensional case. The Wheeler-DeWitt equation is a finite-difference equation. It is exactly solvable in the case of a flat universe and we find the ground state of the system. The closed brane universe can be created as a result of decay of the bulk black hole.     

Quantum mechanics of the early universe

Quantum tunneling of the universe from nothing into a de Sitter vacuum, interpreted as the birth of the universe from a vacuum, is considered. Vilenkin's results are generalized by allowing for strings, domain walls, and various kinds of compressed matter that contribute to the potential through which the tunneling occurs. The energy spectrum of the universe in the quantum pre-de Sitter stage, the coefficient of passage through the potential barrier, which describes the probability of birth of the universe, and the conditions of applicability of the quasi-classical approximation in the calculation of these quantities are found.Brainstorm MNTP, Moscow. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 78–82, April, 1995.     

Quantum creation of multidimensional universes

A non zero probability amplitude for the appearance of a multidimensional universe of (1+d) dimensions is found. This can happen either in a “symmetric phase”, in which all dimensions are in an exponential expansion, or else in a “broken phase”, withd ₁ dimensions inflating exponentially andd ₂ forming a sphere of constant radius. The value of these amplitude for different total number of dimensions is discussed, and so physical consequences for Kaluza-Klein cosmologies are drawn.     

Quantum driven bounce of the future universe

It is demonstrated that due to back-reaction of quantum effects, expansion of the universe stops at its maximum and takes a turn around. Later on, it contracts to a very small size in finite future time. This phenomenon is followed by a “bounce” with re-birth of an exponentially expanding non-singular universe.     

Quantum fluctuations in the new inflationary universe

The evolution of quantum fluctuations of a scalar field in de Sitter space is analyzed in the context of the new inflationary scenario. The duration of the inflationary phase is estimated and the problem of density perturbations resulting from quantum fluctuations of the Higgs field is discussed.     

Quantum mechanics in an entirely deterministic universe

It is argued that, according to the suggested interpretation of quantum mechanical probabilities, (1) the Bell inequalities are not equivalent with those inequalities derived by Pitowsky and others that indicate the Kolmogorovity of a probability model, (2) the original Bell inequalities are irrelevant to both the question of whether or not quantum mechanics is a Kolmogorovian theory as well as the problem of determinism, whereas (3) the Pitowsky-type inequalities are not violated by quantum mechanics, hence (4) quantum mechanics is a Kolmogorovian probability theory, therefore, (5) it is compatible with an entirely deterministic universe.On leave from the Institute for Theoretical Physics, Eötvös University, Budapest, Hungary.     

Stimulated creation of quanta during inflation and the observable universe

Inflation provides a natural mechanism to account for the origin of cosmic structures. The generation of primordial inhomogeneities during inflation can be understood via the spontaneous creation of quanta from the vacuum. We show that when the corresponding stimulated creation of quanta is considered, the characteristics of the state of the universe at the onset of inflation are not diluted by the inflationary expansion and can be imprinted in the spectrum of primordial inhomogeneities. The non-gaussianities (particularly in the so-called squeezed configuration) in the cosmic microwave background and galaxy distribution can then tell us about the state of the universe that existed at the time when quantum field theory in curved spacetime first emerged as a plausible effective theory.     

Quantum effects in “mixmaster universe”

It is shown that under the action of an anisotropic gravitational field nonzero helicity appears in the vacuum state of the massless spinor field. In the hot universe theory it can be interpreted as an origin of baryon or lepton charges in the vacuum. The nonconservation of fermion number in the model is a result of the quantum disintegration of the “charged vacuum” in the process of evolution. The energy-momentum tensor of the created particles and vacuum polarization is calculated.     

Quantum stationary state of class A Bianchi universe

Padmanabhan derived a differential equation for the stationary state for the class A Bianchi model and obtained some approximate solutions. Here we reduce the differential equation to a standard, well-known, solvable linear differential equation and indicate some exact explicit particular solutions.     

Quantum state tomography for generic pure states

We examine the problem of whether a multipartite pure quantum state can be uniquely determined by its reduced density matrices.We show that a generic pure state in three party Hilbert space HA■HB■HC, where dim(HA) = 2 and dim(HB) = dim(HC), can be uniquely determined by its reduced states on subsystems HA■HB and HA■HC. Then, we generalize the conclusion to the case that dim(H_1) 2. As a corollary, we show that a generic N-qudit pure quantum state is uniquely determined by only two of its[(N+1)/2]-particle reduced density matrices. Furthermore,our results indicate a method to uniquely determine a generic N-qudit pure state of dimension D = d~N with only O(D) local measurements, which is an improvement compared to the previous known approach that uses O(D log~2 D) or O(D log D) local measurements.