Analytic discussion of spatially closed friedman universes with cosmological constant and radiation pressure

We derive explicit formulas for various quantities of interest in the universes described in the title, and discuss the interpretation of cosmological constant in quantum field theories.     

The magnetic part of the Weyl tensor,and the expansion of discrete universes

We examine the effect that the magnetic part of the Weyl tensor has on the large-scale expansion of space. This is done within the context of a class of cosmological models that contain regularly arranged discrete masses, rather than a continuous perfect fluid. The natural set of geodesic curves that one should use to consider the cosmological expansion of these models requires the existence of a non-zero magnetic part of the Weyl tensor. We include this object in the evolution equations of these models by performing a Taylor series expansion about a hypersurface where it initially vanishes. At the same cosmological time, measured as a fraction of the age of the universe, we find that the influence of the magnetic part of the Weyl tensor increases as the number of masses in the universe is increased. We also find that the influence of the magnetic part of the Weyl tensor increases with time, relative to the leading-order electric part, so that its contribution to the scale of the universe can reach values of \(\sim \)1%, before the Taylor series approximation starts to break down.     

Nonlinear analysis of irregular animal vocalizations

Animal vocalizations range from almost periodic vocal-fold vibration to completely atonal turbulent noise. Between these two extremes, a variety of nonlinear dynamics such as limit cycles, subharmonics, biphonation, and chaotic episodes have been recently observed. These observations imply possible functional roles of nonlinear dynamics in animal acoustic communication. Nonlinear dynamics may also provide insight into the degree to which detailed features of vocalizations are under close neural control, as opposed to more directly reflecting biomechanical properties of the vibrating vocal folds themselves. So far, nonlinear dynamical structures of animal voices have been mainly studied with spectrograms. In this study, the deterministic versus stochastic (DVS) prediction technique was used to quantify the amount of nonlinearity in three animal vocalizations: macaque screams, piglet screams, and dog barks. Results showed that in vocalizations with pronounced harmonic components (adult macaque screams, certain piglet screams, and dog barks), deterministic nonlinear prediction was clearly more powerful than stochastic linear prediction. The difference, termed low-dimensional nonlinearity measure (LNM), indicates the presence of a low-dimensional attractor. In highly irregular signals such as juvenile macaque screams, piglet screams, and some dog barks, the detectable amount of nonlinearity was comparatively small. Analyzing 120 samples of dog barks, it was further shown that the harmonic-to-noise ratio (HNR) was positively correlated with LNM. It is concluded that nonlinear analysis is primarily useful in animal vocalizations with strong harmonic components (including subharmonics and biphonation) or low-dimensional chaos.     

Brans-Dicke static universes

We study flat and nonflat static models obeying the Brans-Dicke theory and RW metric, including the case which considers Bertolami's time-dependent cosmological term. We find several solutions where the density remains constant, while the gravitational constant varies with time.     

Stability of homogeneous universes

The stability of a class of homogeneous cosmological models is investigated. It is shown that the perturbation problem for six such universes can be reduced to a system of ordinary differential equations. The time development of the perturbations is such that they remain finite at all times for which the unperturbed metric is non-singular.Work supported in part by the National Science Foundation.     

Geometry of multidimensional universes

LetG be a compact group of transformation (global symmetry group) of a manifoldE (multidimensional universe) with all orbits of the same type (one stratum). We studyG invariant metrics onE and show that there is one-to-one correspondence between those metrics and triples (g _μv,A _μ ^ä ,h _αβ), whereg _μv is a (pseudo-) Riemannian metric on the space of orbits (space-time),A _μ ^ä is a Yang-Mills field for the gauge groupN|H, whereN is the normalizer of the isotropy groupH inG, andh _αβ are certain scalar fields characterizing geometry of the orbits (internal spaces). The scalar curvature ofE is expressed in terms of the component fields onM. Examples and model building recipes are also given. The results generalize those of non-abelian Kaluza-Klein theories to the case where internal spaces are not necessarily group manifolds.     

Conformally connected universes

A well-known difficulty associated with the conformal method for the solution of the general relativistic Hamiltonian constraint is the appearance of an aphysical “bag of gold” singularity at the nodal surfaces of the conformal factor. This happens whenever the background Ricci scalar is too large. Using a simple model we demonstrate that some of these singular solutions do have a physical meaning, and that these can be considered as initial data for Universes containing black holes, which are connected, in a conformally nonsingular way with each other. The relation between the ADM mass and the horizon area in this solution supports the cosmic censorship conjecture.     

Auditory profile analysis of irregular sound spectra

The discrimination of changes in the shapes of sound spectra is reported. The change was always an intensity increment to the 948-Hz component of a multitone complex. First, the ability of naive listeners to learn to discriminate a change in a "regular" background or reference spectrum (equal-level tones equally spaced in logarithmic frequency) was measured as a function of the number of trials. On the average, threshold improved about 10 dB over 3000 trials, with about 50% of the decrease in threshold occurring during the first 750 trials. In a subsequent series of experiments, the overall pattern of spectral shape of the background was varied randomly. Two kinds of perturbations in spectral shape were employed: Randomly choosing the frequencies of the reference spectra and randomly choosing the amplitudes of the components of the reference spectra. The experimental manipulations involved fixing the random spectra across a block of trials, varying the reference spectra from interval to interval of each trial, and providing extensive practice in discriminating specific randomly perturbed reference spectra. The results of the spectrum-learning and random perturbation experiments provide insight into the roles of critical band filtering, sensory variability, and short-term and long-term memory representations in auditory profile analysis. Further, the appropriateness of the generalization of a simple energy detection model is discussed.     

On the Stephani universes

The spacetimes corresponding to a weak version of the cosmological principle are considered. It appears that, starting from very different criteria, they were already obtained by Stephani and studied by Krasinski and Barnes. The only barotropic universes of this class are the Friedmann-Robertson-Walker ones. Among the others, some admit a general thermodynamic scheme; it is shown that, as for barotropic fluids, such a scheme also imposes additional symmetries.     

Brane universes with Gauss-Bonnet-induced-gravity

The DGP brane world model allows us to get the observed late time acceleration via modified gravity, without the need for a “dark energy” field. This can then be generalised by the inclusion of high energy terms, in the form of a Gauss-Bonnet bulk. This is the basis of the Gauss-Bonnet-Induced-Gravity (GBIG) model explored here with both early and late time modifications to the cosmological evolution. Recently the simplest GBIG models (Minkowski bulk and no brane tension) have been analysed. Two of the three possible branches in these models start with a finite density “Big-Bang” and with late time acceleration. Here we present a comprehensive analysis of more general models where we include a bulk cosmological constant and brane tension. We show that by including these factors it is possible to have late time phantom behaviour.     

Non-Abelian isometries of multidimensional universes

A field theory on a(d + n)-dimensional manifold in the presence of ann-dimensional isometry group spanningn-dimensional orbit spaces may be reduced to a field theory on ad-dimensional manifold. The field content of such reduced theories is completely worked out when the isometries may be non-Abelian and the resultant space may have torsion. The equations of motion of the dimensionally reduced theory are obtained directly from the higher-dimensional theory. The reduced theory is given in terms of the metric tensor, a set of scalar fields, and a set of antisymmetric tensor fields.Supported in part by the Department of Energy under Contract DE-AS-2-76ER02978 and in part by the National Science Foundation under Grant NSF Phy 83 134 10.     

Anisotropic universes and inflation

Some recent treatment of inflation in anisotropic universes is reviewed and we introduce results related toSO(3) Higgs fields and their influence on the violation of local isotropy.Presented at the International Conference Selected Topics in Quantum Field Theory and Mathematical Physics, Bechyn, Czechoslovakia, June 23–27, 1986.On leave of absence fromU.F.R.J., Inst. de Física, 21940, Rio de Janeiro, Brazil.Working for a Ph. D. degree.     

Spatially homogeneous Lichnerowicz universes

We find in this paper a special class of spatially homogeneous solutions of the Einstein-Lichnerowicz equations, describing the gravitational field of an electrically charged fluid with infinite conductivity.     

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.     

Spacetime averaging of exotic singularity universes

Taking a spacetime average as a measure of the strength of singularities we show that big-rips (type I) are stronger than big-bangs. The former have infinite spacetime averages while the latter have them equal to zero. The sudden future singularities (type II) and w-singularities (type V) have finite spacetime averages. The finite scale factor (type III) singularities for some values of the parameters may have an infinite average and in that sense they may be considered stronger than big-bangs.     

Friedmann universes containing wave fields

In this paper the Friedmann universes containing(i) a massless real scalar field,(ii) a massive real scalar field,(iii) electromagnetic fields,(iv) the combined massive complex scalar and electromagnetic fields are investigated. In(i) the field has to be either purely spatial or else purely temporal and the latter case is completely solved. Similarly in(ii) the purely time-dependent case has been reduced to a single fourth order ordinary differential equation. In this case graphs of the numerical solutions have been exhibited. In(iii) as expected, no non-trivial solution exists. In(iv) all possible cases are studied. In case the complex wave function is a product of two non-constant functions, i.e. ψ=ξ(r)τ(t), there exists no solution. In the subcase gx(r)=ξ^*(r)=constant, ¦τ(t)¦=constant the problem is completely solved. In the subcase ξ(r)=ξ^*(r)=constant and ¦τ(t)¦ is non-constant, the system of equations boil down to the same fourth order ordinary differential equation as mentioned before. In the last two sub-cases, the time-dependent wave field carries electric charge density which, strangely enough, is decoupled from the electromagnetic fields.