Note on equivalence of cosmological space-times

It is shown that only de Sitter space and Minkowski space can be expressed in more than one of the standard forms for Robertson-Walker space-times.     

Self-dual space-times with cosmological constant

It is shown that self-dual solutions of Einstein's equations, with cosmological constant , correspond to certain complex manifolds. This result generalizes the work of Penrose [1], who dealt with the case =0.     

A computer code for the study of spherically-symmetric cosmological space-times

We describe an Eulerian, explicit computer code for the study of spherically-symmetric cosmological space-times on a Robertson-Walker background. The Einstein equations and the relativistic-hydrodynamic equations are written down for such a space-time using the 3+1 formalism of Arnowitt, Deser, and Misner [1]. Time slices are selected by the constant-mean-curvature criterion. Numerical techniques utilized in the code, as well as several code tests, are discussed, with emphasis on the difficulties encountered and their possible causes and cures.     

Properties of the quantum universe in quasistationary states and cosmological puzzles

Old and new puzzles of cosmology are reexamined from the point of view of the quantum theory of the universe developed here. It is shown that in the proposed approach the difficulties of the standard cosmology do not arise. The theory predicts the observed dimensions of the non-homogeneities of matter density and the amplitude of fluctuations of the cosmic background radiation temperature in the Universe and points to a new quantum mechanism of their origin. The large-scale structure in the Universe is explained by the growth of non-homogeneities which arise from primordial quantum fluctuations due to the finite width of the quasistationary states. The theory allows one to obtain the value of the deceleration parameter, which is in good agreement with the recent SNe Ia measurements. It explains the large value of the entropy of the Universe and describes other parameters. Received: 30 July 2001 / Published online: 8 February 2002     

A quantum cosmological model based on Einstein's universe

The conformal factor and a massless scalar field are quantized on Einstein background spacetime. A singularity-free cosmological model is obtained and discussed.     

The graviton one-loop effective action in cosmological space-times with constant deceleration

We consider the quantum Friedmann equations which include one-loop vacuum fluctuations due to gravitons and scalar field matter in a FLRW background with constant . After several field redefinitions, to remove the mixing between the gravitational and matter degrees of freedom, we can construct the one-loop correction to the Friedmann equations. Due to cosmological particle creation, the propagators needed in such a calculation are typically infrared divergent. In this paper we construct the graviton and matter propagators, making use of the recent construction of the infrared finite scalar propagators calculated on a compact spatial manifold in Janssen et al. (2008) [1]. The resulting correction to the Friedman equations is suppressed with respect to the tree level contribution by a factor of and shows no secular growth.     

A general framework for cosmological quantum theory

A self-contained structure for interpreting quantum theory in a cosmological context is presented which is free from the “unique predecessor” restriction previously imposed, and which allows mixed states involving only a finite part of the universe.     

A fundamental constraint on quantum mechanical diffusion coefficients

A general quantum mechanical master equation for the damped oscillator, which can be represented as a phase space Fokker-Planck equation for the Wigner function, will be investigated with respect to the uncertainty principle. This leads to a condition to be imposed on the diffusion coefficients, which (i) is not fulfilled by an often quoted quasi-classical choice, and (ii) provides a uniqueness criterium in Dekker's theory.     

Non-singular space-times with a negative cosmological constant: V. Boson stars

We prove existence of large families of solutions of Einstein-complex scalar field equations with a negative cosmological constant, with a stationary or static metric and a time-periodic complex scalar field.     

Partition functions and physical states in two-dimensional quantum gravity and supergravity

We review the Liouville theory calculation of the genus-one path integral for c 1 conformal models coupled to two-dimensional gravity. From the modular integrand we derive the existence of an infinite number of physical operators which are in one-to-one correspondence with the conformal primary fields and null states of the matter theory. We also calculate the torus path integral and find the spectrum of physical operators for superconformal models coupled to supergravity. The amplitude in the odd spin structure requires a special treatment and is found to be proportional to the Witten index of the matter theory.     

Renormalization-group analysis of the cosmological constraint on the Higgs scalar mass

The standard Model Higgs scalar boson minimally coupled to gravity does not take part in the inflation of the early universe if its mass exceeds a threshold value, which is m _H ^min = 142 GeV in the tree approximation for the potential of the scalar. Two-loop corrections modify this estimate, which becomes m _H ^min = 150 ± 3 GeV. Therefore, higher order corrections of perturbation theory have quite a controllable moderate character, but they are numerically important for experiments.     

Doubling of states, quantum anomalies, and possible cosmological consequences in the continuum limit of the theory of discrete quantum gravity

The problem of the doubling of states is investigated in the framework of the theory of discrete quantum gravity under the assumption that the theory has a continuum (macroscopic) limit. It is demonstrated that irregular (in some sense) modes of fields (i.e., modes that change abruptly on scales of a lattice step and have a finite energy when the lattice step tends to zero) are separated from the normal modes. Some cosmological consequences of this finding are discussed.     

Remarks on quantum field theory on de Sitter and anti-de Sitter space-times

This is a short review of work done in common with Jacques Bros, Michel Gaudin, Ugo Moschella, and Vincent Pasquier. Among results are explicit K?llén?CLehmann representations for products of two free-field two-point functions in the de Sitter and the anti-de Sitter spaces and applications to particle decay.     

The hypergeneralized Heun equation in quantum field theory in curved space-times

We show for the first time the role played by the hypergeneralized Heun equation (HHE) in the context of quantum field theory in curved space-times. More precisely, we find suitable transformations relating the separated radial and angular parts of a massive Dirac equation in the Kerr-Newman-deSitter metric to a HHE.     

Gravitational and quantum effects in rotating cosmological models

Specific effects of the dynamics of (spinor and scalar) wave fields are considered in rotating uniform Gödel-type cosmological models. It is shown that the gravitational interaction of the spinor field can be reduced to the interaction between its pseudovector current and the angular velocity of space-time rotation and is similar to its interaction with the pseudotrace of the space-time twisting. The mean values of energy-momentum tensor of the quantized scalar field in vacuum are calculated in rotating cosmological models and the difference between these values and their mean counterparts in vacuum is determined for Friedman's nonrotating cosmological models.State Education Institute, Yaroslavl'. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 35–38, June, 1992.     

Interacting quantum fields in a nonsingular cosmological model

The density of massless vector bosons created in a conformally flat nonsingular cosmological model is calculated.     

On the induced cosmological term in quantum gravity

Tadpole diagrams where zero-momentum gravitons couple to massive matter loops lead to divergences which are not a consequence of infinite momentum integrals, but of the masslessness of the gravitons. It is shown that there exists no definition of these diagrams consistent with the Ward identities. They can be eliminated by an appropriate gauge choice, but then the BRS symmetry is spontaneously broken. Also in the scalar-tensor, conformally invariant formulation of quantum gravity, the tadpole problem does survive. The tadpole diagrams can, however, be cancelled by a cosmological counter-term. In that case, the Ward identities are satisfied.