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 gravitational waves in the light of 7-year Wilkinson Microwave Anisotropy Probe data and improved prospects for the Planck mission

The new release of data from Wilkinson Microwave Anisotropy Probe improves the observational status of relic gravitational waves. The 7-year results enhance the indications of relic gravitational waves in the existing data and change to the better the prospects of confident detection of relic gravitational waves by the currently operating Planck satellite. We apply to WMAP7 data the same methods of analysis that we used earlier [W. Zhao, D. Baskaran, and L.P. Grishchuk, Phys. Rev. D 80, 083005 (2009)] with WMAP5 data. We also revised by the same methods our previous analysis of WMAP3 data. It follows from the examination of consecutive WMAP data releases that the maximum likelihood value of the quadrupole ratio $R$, which characterizes the amount of relic gravitational waves, increases up to $R=0.264$, and the interval separating this value from the point $R=0$ (the hypothesis of no gravitational waves) increases up to a $2\sigma$ level. The primordial spectra of density perturbations and gravitational waves remain blue in the relevant interval of wavelengths, but the spectral indices increase up to $n_s =1.111$ and $n_t=0.111$. Assuming that the maximum likelihood estimates of the perturbation parameters that we found from WMAP7 data are the true values of the parameters, we find that the signal-to-noise ratio $S/N$ for the detection of relic gravitational waves by the Planck experiment increases up to $S/N=4.04$, even under pessimistic assumptions with regard to residual foreground contamination and instrumental noises. We comment on theoretical frameworks that, in the case of success, will be accepted or decisively rejected by the Planck observations.Comment: 27 pages, 12 (colour) figures. Published in Phys. Rev. D. V.3: modifications made to reflect the published versio

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

Components of the gravitational force in the field of a gravitational wave

Gravitational waves bring about the relative motion of free test masses. The detailed knowledge of this motion is important conceptually and practically, because the mirrors of laser interferometric detectors of gravitational waves are essentially free test masses. There exists an analogy between the motion of free masses in the field of a gravitational wave and the motion of free charges in the field of an electromagnetic wave. In particular, a gravitational wave drives the masses in the plane of the wave-front and also, to a smaller extent, back and forth in the direction of the wave's propagation. To describe this motion, we introduce the notion of `electric' and `magnetic' components of the gravitational force. This analogy is not perfect, but it reflects some important features of the phenomenon. Using different methods, we demonstrate the presence and importance of what we call the `magnetic' component of motion of free masses. It contributes to the variation of distance between a pair of particles. We explicitely derive the full response function of a 2-arm laser interferometer to a gravitational wave of arbitrary polarization. We give a convenient description of the response function in terms of the spin-weighted spherical harmonics. We show that the previously ignored `magnetic' component may provide a correction of up to 10 %, or so, to the usual `electric' component of the response function. The `magnetic' contribution must be taken into account in the data analysis, if the parameters of the radiating system are not to be mis-estimated.Comment: prints to 29 pages including 9 figures, new title, additional explanations and references in response to referee's comments, to be published in Class. Quant. Gra

Separating E and B types of polarization on an incomplete sky

Detection of magnetic-type ($B$-type) polarization in the Cosmic Microwave Background (CMB) radiation plays a crucial role in probing the relic gravitational wave (RGW) background. In this paper, we propose a new method to deconstruct a polarization map on an incomplete sky in real space into purely electric and magnetic polarization type maps, ${\mathcal{E}}(\hat{\gamma})$ and ${\mathcal{B}}(\hat{\gamma})$, respectively. The main properties of our approach are as follows: Firstly, the fields ${\mathcal{E}}(\hat{\gamma})$ and ${\mathcal{B}}(\hat{\gamma})$ are constructed in real space with a minimal loss of information. This loss of information arises due to the removal of a narrow edge of the constructed map in order to remove various numerical errors, including those arising from finite pixel size. Secondly, this method is fast and can be efficiently applied to high resolution maps due to the use of the fast spherical harmonics transformation. Thirdly, the constructed fields, ${\mathcal{E}}(\hat{\gamma})$ and ${\mathcal{B}}(\hat{\gamma})$, are scalar fields. For this reason various techniques developed to deal with temperature anisotropy maps can be directly applied to analyze these fields. As a concrete example, we construct and analyze an unbiased estimator for the power spectrum of the $B$-mode of polarization $C_{\ell}^{BB}$. Basing our results on the performance of this estimator, we discuss the RGW detection ability of two future ground-based CMB experiments, QUIET and POLARBEAR.Comment: 43 pages, 15 figures, 1 table. The finial version, will appear in PR

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

Is the squeezing of relic gravitational waves produced by inflation detectable?

Grishchuk has shown that the stochastic background of gravitational waves produced by an inflationary phase in the early Universe has an unusual property: it is not a stationary Gaussian random process. Due to squeezing, the phases of the different waves are correlated in a deterministic way, arising from the process of parametric amplification that created them. The resulting random process is Gaussian but non-stationary. This provides a unique signature that could in principle distinguish a background created by inflation from stationary stochastic backgrounds created by other types of processes. We address the question: could this signature be observed with a gravitational wave detector? Sadly, the answer appears to be "no": an experiment which could distinguish the non-stationary behavior would have to last approximately the age of the Universe at the time of measurement. This rules out direct detection by ground and space based gravitational wave detectors, but not indirect detections via the electromagnetic Cosmic Microwave Background Radiation (CMBR).Comment: 17 pages, 4 Postscript figures, uses revtex, psfig, to be submitted to PRD, minor revisions - appendix B clarified, corrected typos, added reference

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 $\epsilon\lesssim 2\cdot 10^{-2}$