Mixmaster Chaoticity as Semiclassical Limit of the Canonical Quantum Dynamics

Within a cosmological framework, we provide a Hamiltonian analysis of the Mixmaster Universe dynamics on the base of a standard Arnowitt-Deser-Misner approach, showing how the chaotic behavior characterizing the evolution of the system near the cosmological singularity can be obtained as the semiclassical limit of the canonical quantization of the model in the same dynamical representation. The relation between this intrinsic chaotic behavior and the indeterministic quantum dynamics is inferred through the coincidence between the microcanonical probability distribution and the semiclassical quantum one.Comment: 9 pages, 1 figur

Gravity Waves Signatures from Anisotropic pre-Inflation

We show that expanding or contracting Kasner universes are unstable due to the amplification of gravitational waves (GW). As an application of this general relativity effect, we consider a pre-inflationary anisotropic geometry characterized by a Kasner-like expansion, which is driven dynamically towards inflation by a scalar field. We investigate the evolution of linear metric fluctuations around this background, and calculate the amplification of the long-wavelength GW of a certain polarization during the anisotropic expansion (this effect is absent for another GW polarization, and for scalar fluctuations). These GW are superimposed to the usual tensor modes of quantum origin from inflation, and are potentially observable if the total number of inflationary e-folds exceeds the minimum required to homogenize the observable universe only by a small margin. Their contribution to the temperature anisotropy angular power spectrum decreases with the multipole l as l^(-p), where p depends on the slope of the initial GW power-spectrum. Constraints on the long-wavelength GW can be translated into limits on the total duration of inflation and the initial GW amplitude. The instability of classical GW (and zero-vacuum fluctuations of gravitons) during Kasner-like expansion (or contraction) may have other interesting applications. In particular, if GW become non-linear, they can significantly alter the geometry before the onset of inflation

Heating up the cold bounce

Self-dual string cosmological models provide an effective example of bouncing solutions where a phase of accelerated contraction smoothly evolves into an epoch of decelerated Friedmann--Robertson--Walker expansion dominated by the dilaton. While the transition to the expanding regime occurs at sub-Planckian curvature scales, the Universe emerging after the bounce is cold, with sharply growing gauge coupling. However, since massless gauge bosons (as well as other massless fields) are super-adiabatically amplified, the energy density of the maximally amplified modes re-entering the horizon after the bounce can efficiently heat the Universe. As a consequence the gauge coupling reaches a constant value, which can still be perturbative.Comment: 28 pages, 13 figure

An Overview of the Anomaly-Induced Inflation

The anomaly-induced inflation (modified Starobinsky model) is based on the application of the effective quantum field theory approach to the Early Universe. We present a brief general review of this model with a special attention to the existing difficulties and unsolved problems.Comment: Talk presented at IRGA2003 (Renormalization Group and Anomalies in Gravitation and Cosmology, Ouro Preto, Brazil, 16-23 March, 2003

Lambda-inflation and CMB anisotropy

We explore a broad class of three-parameter inflationary models, called the $\Lambda$-inflation, and its observational predictions: high abundance of cosmic gravitational waves consistent with the Harrison-Zel'dovich spectrum of primordial cosmological perturbations, the non-power-law wing-like spectrum of matter density perturbations, high efficiency of these models to meet current observational tests, and others. We show that a parity contribution of the gravitational waves and adiabatic density perturbations into the large-scale temperature anisotropy, T/S $\sim 1$, is a common feature of $\Lambda$-inflation; the maximum values of T/S (basically not larger than 10) are reached in models where (i) the local spectrum shape of density perturbations is flat or slightly red ($n_S{}_\sim^< 1$), and (ii) the residual potential energy of the inflaton is near the GUT scale ($V_0^{{1/4}} \sim 10^{16} GeV$). The conditions to find large T/S in the paradigm of cosmic inflation and the relationship of T/S to the ratio of the power spectra, $r$, and to the inflationary $\gamma$ and Hubble parameters, are discussed. We argue that a simple estimate, T/S$\simeq 3r\simeq 12\gamma \simeq (\frac{H}{6\times 10^{13}{\rm GeV}})^2$, is true for most known inflationary solutions and allows to relate straightforwardly the important parameters of observational and physical cosmology.Comment: 29 pages, 3 figures include

Relation Between Einstein And Quantum Field Equations

We show that there exists a choice of scalar field modes, such that the evolution of the quantum field in the zero-mass and large-mass limits is consistent with the Einstein equations for the background geometry. This choice of modes is also consistent with zero production of these particles and thus corresponds to a preferred vacuum state preserved by the evolution. In the zero-mass limit, we find that the quantum field equation implies the Einstein equation for the scale factor of a radiation-dominated universe; in the large-mass case, it implies the corresponding Einstein equation for a matter-dominated universe. Conversely, if the classical radiation-dominated or matter-dominated Einstein equations hold, there is no production of scalar particles in the zero and large mass limits, respectively. The suppression of particle production in the large mass limit is over and above the expected suppression at large mass. Our results hold for a certain class of conformally ultrastatic background geometries and therefore generalize previous results by one of us for spatially flat Robertson-Walker background geometries. In these geometries, we find that the temporal part of the graviton equations reduces to the temporal equation for a massless minimally coupled scalar field, and therefore the results for massless particle production hold also for gravitons. Within the class of modes we study, we also find that the requirement of zero production of massless scalar particles is not consistent with a non-zero cosmological constant. Possible implications are discussed.Comment: Latex, 24 pages. Minor changes in text from original versio

On generation of metric perturbations during preheating

We consider the generation of the scalar mode of the metric perturbations during preheating stage in a two field model with the potential $V(\phi, \chi)= {m^{2}\phi^{2}\over 2}+{g^{2}\phi^{2}\chi^{2}\over 2}$. We discuss two possible sources of such perturbations: a) due to the coupling between the perturbation of the matter field $\delta \chi$ and the background part of the matter field $\chi_{0}(t)$, b) due to non-linear fluctuations in a condensate of ``particles'' of the field $\chi$. Both types of the metric perturbations are assumed to be small, and estimated using the linear theory of the metric perturbations. We estimate analytically the upper limit of the amplitude of the metric perturbations for all scales in the limit of so-called broad resonance, and show that the large scale metric perturbations are very small, and taking them into account does not influence the standard picture of the production of the metric perturbations in inflationary scenario.Comment: This version is to be published in PRD, new references added and typos correcte

The Implications of the Microwave Background Anisotropies for Laser-Interferometer-Tested Gravitational Waves

The observed microwave background anisotropies in combination with the theory of quantum mechanically generated cosmological perturbations predict a well measurable amount of relic gravitational waves in the frequency intervals tested by LISA and ground-based laser interferometers.Comment: revised, corrected, and slightly expanded version to be published in Classical and Quantum Gravity; 22 pages, 1 Postscript figure, Latex; Based on a talk presented at the First Internationsl LISA Symposium, 9 - 12 July 1996, RAL, U

Imprints of Relic Gravitational Waves in Cosmic Microwave Background Radiation

A strong variable gravitational field of the very early Universe inevitably generates relic gravitational waves by amplifying their zero-point quantum oscillations. We begin our discussion by contrasting the concepts of relic gravitational waves and inflationary `tensor modes'. We explain and summarize the properties of relic gravitational waves that are needed to derive their effects on CMB temperature and polarization anisotropies. The radiation field is characterized by four invariants I, V, E, B. We reduce the radiative transfer equations to a single integral equation of Voltairre type and solve it analytically and numerically. We formulate the correlation functions C^{XX'}_{\ell} for X, X'= T, E, B and derive their amplitudes, shapes and oscillatory features. Although all of our main conclusions are supported by exact numerical calculations, we obtain them, in effect, analytically by developing and using accurate approximations. We show that the TE correlation at lower \ell's must be negative (i.e. an anticorrelation), if it is caused by gravitational waves, and positive if it is caused by density perturbations. This difference in TE correlation may be a signature more valuable observationally than the lack or presence of the BB correlation, since the TE signal is about 100 times stronger than the expected BB signal. We discuss the detection by WMAP of the TE anticorrelation at \ell \approx 30 and show that such an anticorrelation is possible only in the presence of a significant amount of relic gravitational waves (within the framework of all other common assumptions). We propose models containing considerable amounts of relic gravitational waves that are consistent with the measured TT, TE and EE correlations.Comment: 61 pages including 15 figures, v.2: additional references and clarifications, to be published in Phys. Rev.

Relic Gravitons, Dominant Energy Condition and Bulk Viscous Stresses

If the energy momentum tensor contains bulk viscous stresses violating the dominant energy condition (DOC) the energy spectra of the relic gravitons (produced at the time of the DOC's violation) increase in frequency in a calculable way. In a general relativistic context we give examples where the DOC is only violated for a limited amount of time after which the ordinary (radiation dominated) evolution takes place. We connect our discussion to some recent remarks of Grishchuk concerning the detectability of the stochastic gravitational wave background by the forthcoming interferometric detectors.Comment: 7 pages in LaTex style. Accepted for publication in Phys. Rev. D (Rapid Comm.