Quantum Effects In Cosmology

Contents: Introduction. The Present State of the Universe. What Can We Expect From a Complete Cosmological Theory? An Overview of Quantum Effects in Cosmology. Parametric (Superadiabatic) Amplification of Classical Waves. Graviton Creation in the Inflationary Universe. Quantum States of a Harmonic Oscillator. Squeezed Quantum States of Relic Gravitons and Primordial Density Perturbations. Quantum Cosmology, Minisuperspace Models and Inflation. From the Space of Classical Solutions to the Space of Wave Functions. On the Probability of Quantum Tunneling From "Nothing". Duration of InflationComment: (43 pages, to be published in "The Origin of Structure in the Universe", ed. P.Nardone

Cosmological Perturbations of Quantum-Mechanical Origin and Anisotropy of the Microwave Background

Cosmological perturbations generated quantum-mechanically (as a particular case, during inflation) possess statistical properties of squeezed quantum states. The power spectra of the perturbations are modulated and the angular distribution of the produced temperature fluctuations of the CMBR is quite specific. An exact formula is derived for the angular correlation function of the temperature fluctuations caused by squeezed gravitational waves. The predicted angular pattern can, in principle, be revealed by the COBE-type observations.Comment: 9 pages, WUGRAV-92-17 Accepted for Publication in Phys. Rev. Letters (1993

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.

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

The surfing effect in the interaction of electromagnetic and gravitational waves. Limits on the speed of gravitational waves

In the current work we investigate the propagation of electromagnetic waves in the field of gravitational waves. Starting with simple case of an electromagnetic wave travelling in the field of a plane monochromatic gravitational wave we introduce the concept of surfing effect and analyze its physical consequences. We then generalize these results to an arbitrary gravitational wave field. We show that, due to the transverse nature of gravitational waves, the surfing effect leads to significant observable consequences only if the velocity of gravitational waves deviates from speed of light. This fact can help to place an upper limit on the deviation of gravitational wave velocity from speed of light. The micro-arcsecond resolution promised by the upcoming precision interferometry experiments allow to place stringent upper limits on $\epsilon = (v_{gw}-c)/c$ as a function of the energy density parameter for gravitational waves $\Omega_{gw}$. For $\Omega_{gw} \approx 10^{-10}$ this limit amounts to $\epsilon\lesssim 2\cdot 10^{-2}$

Sensitivity of a VIRGO pair to stochastic GW backgrounds

The sensitivity of a pair of VIRGO interferometers to gravitational waves backgrounds (GW) of cosmological origin is analyzed for the cases of maximal and minimal overlap of the two detectors. The improvements in the detectability prospects of scale-invariant and non-scale-invariant logarithmic energy spectra of relic GW are discussed.Comment: 25 pages in RevTex style with 6 figure

Parametric amplification of waves during gravitational collapse: a first investigation

We study the dynamical evolution of perturbations in the gravitational field of a collapsing fluid star. Specifically, we consider the initial value problem for a massless scalar field in a spacetime similar to the Oppenheimer-Snyder collapse model, and numerically evolve in time the relevant wave equation. Our main objective is to examine whether the phenomenon of parametric amplification, known to be responsible for the strong amplification of primordial perturbations in the expanding Universe, can efficiently operate during gravitational collapse. Although the time-varying gravitational field inside the star can, in principle, support such a process, we nevertheless find that the perturbing field escapes from the star too early for amplification to become significant. To put an upper limit in the efficiency of the amplification mechanism (for a scalar field) we furthermore consider the case of perturbations trapped inside the star for the entire duration of the collapse. In this extreme case, the field energy is typically amplified at the level ~ 1% when the star is about to cross its Schwarszchild radius. Significant amplification is observed at later stages when the star has even smaller radius. Therefore, the conclusion emerging from our simple model is that parametric amplification is unlikely to be of significance during gravitational collapse. Further work, based on more realistic collapse models, is required in order to fully assess the astrophysical importance of parametric amplification.Comment: 14 pages, revtex, 9 eps figure

Density Perturbations of Quantum Mechanical Origin and Anisotropy of the Microwave Background

If the large-angular-scale anisotropy in the cosmic microwave background radiation is caused by the long-wavelength cosmological perturbations of quantum mechanical origin, they are, most likely, gravitational waves, rather than density perturbations or rotational perturbations.Comment: 53 pages, RevTeX, WUGRAV-94-4, (Received by Phys. Rev. D on March 17, 1994

On the observational determination of squeezing in relic gravitational waves and primordial density perturbations

We develop a theory in which relic gravitational waves and primordial density perturbations are generated by strong variable gravitational field of the early Universe. The generating mechanism is the superadiabatic (parametric) amplification of the zero-point quantum oscillations. The generated fields have specific statistical properties of squeezed vacuum quantum states. Macroscopically, squeezing manifests itself in a non-stationary character of variances and correlation functions of the fields, the periodic structures of the metric power spectra, and, as a consequence, in oscillatory behavior of the higher order multipoles C_l of the cosmic microwave background anisotropy. We start with the gravitational wave background and then apply the theory to primordial density perturbations. We derive an analytical formula for the positions of peaks and dips in the angular power spectrum l(l+1)C_l as a function of l. This formula shows that the values of l at the peak positions are ordered in the proportion 1:3:5:..., whereas at the dips they are ordered as 1:2:3:.... We compare the derived positions with the actually observed features, and find them to be in reasonably good agreement. It appears that the observed structure is better described by our analytical formula based on the (squeezed) metric perturbations associated with the primordial density perturbations, rather than by the acoustic peaks reflecting the existence of plasma sound waves at the last scattering surface. We formulate a forecast for other features in the angular power spectrum, that may be detected by the advanced observational missions, such as MAP and PLANCK. We tentatively conclude that the observed structure is a macroscopic manifestation of squeezing in the primordial metric perturbations.Comment: 34 pages, 3 figures; to appear in Phys. Rev. D66, 0435XX (2002); includes Note Added in Proofs: "The latest CBI observations (T.J.Pearson et al., astro-ph/0205388) have detected four peaks, at l ~ 550, 800, 1150, 1500, and four dips, at l ~ 400, 700, 1050, 1400. These positions are in a very good agreement with the theoretical formula (6.35) of the present paper. We interpret this data as confirmation of our conclusion that it is gravity, and not acoustics, that is responsible for the observed structure.