Absence of a singularity in loop quantum cosmology

It is shown that the cosmological singularity in isotropic minisuperspaces is naturally removed by quantum geometry. Already at the kinematical level, this is indicated by the fact that the inverse scale factor is represented by a bounded operator even though the classical quantity diverges at the initial singularity. The full demonstration comes from an analysis of quantum dynamics. Because of quantum geometry, the quantum evolution occurs in discrete time steps and does not break down when the volume becomes zero. Instead, space-time can be extended to a branch preceding the classical singularity independently of the matter coupled to the model. For large volume the correct semiclassical behavior is obtained.     

On the initial singularity in the scalar-tensor anisotropic cosmology

In connection with the problem of the initial singularity in the scalar-tensor anisotropic cosmology of Jordan-Brans-Dicke, the dynamics of homogeneous models of Bianchi type I is examined on the basis of the general analytic solutions in vacuo and in the presence of gravitating matter with state equations P=n? (0 ? n ? 1). It is shown that the scalar homogeneous ?-field, as an effective source of the V₄geometry, has to influence essentially the dynamics of the early anisotropic stage of the Universe's expansion, and significantly modifies the character of the initial singularity. At negative ω (ω < ?6), the sourceless scalar ?-field may remove the singularity and provide regular ‘bouncing’ in the models with matter (P ? ?/3) if it prevails over the tensor anisotropic mode of the vacuum gravitational field.     

Fermi-edge singularity in the vicinity of the resonant scattering condition

Fermi-edge absorption theory predicting the spectrum A(ω) ∝ ω(-2δ(0)/π+δ(0)92)/π2) relies on the assumption that scattering phase δ(0) is frequency independent. The dependence of δ(0) on ω becomes crucial near the resonant condition, where the phase changes abruptly by π. In this limit, because of the finite time spent by electron on a resonant level, the scattering is dynamic. We incorporate the finite time delay into the theory, solve the Dyson equation with a modified kernel, and find that, near the resonance, A(ω) behaves as ω(-3/4)|lnω|. Scattering off the core hole becomes resonant in 1D and 2D in the presence of an empty subband above the Fermi level; then a deep hole splits off a level from the bottom of this subband. Fermi-edge absorption in the regime when resonant level transforms into a Kondo peak is discussed.     

Casimir effects near the big rip singularity in viscous cosmology

Analytical properties of the scalar expansion in the cosmic fluid are investigated, especially near the future singularity, when the fluid possesses a constant bulk viscosity ζ. In addition, we assume that there is a Casimir-induced term in the fluid’s energy-momentum tensor, in such a way that the Casimir contributions to the energy density and pressure are both proportional to 1/a ⁴, a being the scale factor. A series expansion is worked out for the scalar expansion under the condition that the Casimir influence is small. Close to the Big Rip singularity the Casimir term has however to fade away and we obtain the same singular behavior for the scalar expansion, the scale factor, and the energy density, as in the Casimir-free viscous case.     

Stochastic behavior of multidimensional cosmological models near a singularity

NITsPV. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 107–111, November, 1994.     

A multidimensional extension of the Bianchi type-IX cosmology

A higher-dimensional homogeneous spacetime is investigated satisfying the vacuum Einstein equations. It is assumed that the algebra of Killing vectors L admits a non-trivial Levi decomposition L = N ⨴so(3), i.e. that the subalgebras N and so(3) do not commute. It is found that the model behaves in a non-chaotic way and cosmological dimensional reduction inevitably occurs. This model completes all the possible types within the class of higher-dimensional extensions of Bianchi type-IX cosmology.     

A scalar field with self-interaction leads to the absence of a singularity in cosmology

A self-consistent treatment of the Higgs conformal field with spontaneously broken symmetry and gravitational field in the semiclassical approximation is shown (by computer calculations) to lead to the absence of a singularity in the anisotropic model if the domain structure is taken into account.     

The vanishing likelihood of space-time singularity in quantum conformal cosmology

A general formalism is developed for studying the behavior of quantized conformal fluctuations near the space-time singularity of classical relativistic cosmology. It is shown that if the material contents of space-time are made of massive particles which obey the principle of asymptotic freedom and interact only gravitationally, then it is possible to estimate the quantum mechanical probability that, of the various possible conformal transforms of the classical Einstein solution, the actual model had a singularity in the past. This probability turns out to be vanishingly small, thus indicating that within the regime of quantum conformal cosmology it is extremely unlikely that the universe originated out of a space-time singularity.     

Quantum fluctuations and nonavoidance of the singularity in Bianchi type I cosmology

An effective metric is defined and used for analyzing the quantum fluctuations in a classical geometry. Earlier work showing that quantum (conformal) fluctuations avoid the classical singularity in the case of spherically symmetric collapse is briefly reviewed. It is shown that this result doesnot extend to anisotropic Bianchi type I cosmology. Here the dispersion in the fluctuations increases too slowly to quench the classical singularity. The singularity persists in the space-time described by the effective metric.     

Dimensional reduction and the stability problem in multidimensional homogeneous cosmology

We show the noneffectiveness of the classical mechanism of the dynamical reduction within the class of arbitrary-dimensional homogeneous cosmological models. The stability of solutions with the static microspace within the class of Bianchi (withn _a ^a =0) × T^D models is also discussed.     

The problems of singularity particle horizon and flatness in quantum cosmology

Classical relativistic cosmology is known to have the space-time singularity as an inevitable feature. The standard big bang models have very small particle horizons in the early stages which make it difficult to understand the observed homogeneity in the universe. The relatively narrow range of the observed matter density in the neighbourhood of closure density requires highly fine tuning of the early universe. In this paper it is argued that these three problems can be satisfactorily resolved in quantum cosmology. It is shown that it is extremely unlikely that the universe evolved to the present state from quantum states with singularity and particle horizon. Similarly, it is shown that of all possible states the Robertson-Walker model of flat spatial sections is the most likely state for the universe to evolve out of a quantum fluctuation. To demonstrate these results a suitable formalism for quantum cosmology is first developed.     

Dynamics of k-essence in loop quantum cosmology

In this paper,we study the dynamics of k-essence in loop quantum cosmology(LQC).The study indicates that the loop quantum gravity(LQG)effect plays a key role only in the early epoch of the universe and is diluted in the later stages.The fixed points in LQC are basically consistent with those in standard Friedmann-Robertson-Walker(FRW)cosmology.For most of the attractor solutions,the stability conditions in L Q C are in agreement with those for the standard FRW universe.For some special fixed points,however,tighter constraints are imposed thanks to the LQG effect.     

Are Einstein's equations of homogeneous multidimensional cosmology generic?

It is shown that Einstein's equations for multidimensional homogeneous block diagonal cosmology are generic only if the dimension of space-time is 4.     

Logarithmic singularity in the specific heat in the vicinity of phase transitions in uniaxial ferroelectrics

Using precise vacuum adiabatic calorimetry it is shown that the specific heat of the model ferroelectric crystal TGS does not exhibit the logarithmic singularity predicted by theory above the transition temperature. This discrepancy with the available specific heat data in the literature, obtained by dynamical measurements, is discussed with allowance for the maximum attainable measurement accuracy (0.3%) in the static adiabatic experiment. Fiz. Tverd. Tela (St. Petersburg) 40, 106–108 (January 1998)