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Register a new userSpectrum of relic gravitational waves in string cosmology
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We compute the spectrum of relic gravitons in a model of string cosmology. In the low- and in the high-frequency limits we reproduce known results. The full spectrum, however, also displays a series of oscillations which could give a characteristic signature at the planned LIGO/VIRGO detectors. For special values of the parameters of the model the signal reaches its maximum already at frequencies accessible to LIGO and VIRGO and it is close to the sensitivity of first generation experiments.
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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 ells 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.
The spectrum of relic gravitational wave (RGW) contains high-frequency divergences, which should be removed. We present a systematic study of the issue, based on the exact RGW solution that covers the five stages, from inflation to the acceleration, each being a power law expansion. We show that the present RGW consists of vacuum dominating at $f>10^{11}$Hz and graviton dominating at $f<10^{11}$Hz, respectively. The gravitons are produced by the four cosmic transitions, mostly by the inflation-reheating one. We perform adiabatic regularization to remove vacuum divergences in three schemes: at present, at the end of inflation, and at horizon-exit, to the 2-nd adiabatic order for the spectrum, and the 4-th order for energy density and pressure. In the first scheme a cutoff is needed to remove graviton divergences. We find that all three schemes yield the spectra of a similar profile, and the primordial spectrum defined far outside horizon during inflation is practically unaffected. We also regularize the gauge-invariant perturbed inflaton and the scalar curvature perturbation by the last two schemes, and find that the scalar spectra, the tensor-to-scalar ratio, and the consistency relation remain unchanged.
The authority of J. A. Wheeler in many areas of gravitational physics is immense, and there is a connection with the study of relic gravitational waves as well. I begin with a brief description of Wheelers influence on this study. One part of the paper is essentially a detailed justification of the very existence of relic gravitational waves, account of their properties related to the quantum-mechanical origin, derivation of the expected magnitude of their effects, and reasoning why they should be detectable in the relatively near future. This line of argument includes the comparison of relic gravitational waves with density perturbations of quantum-mechanical origin, and the severe criticism of methods and predictions of inflationary theory. Another part of the paper is devoted to active searches for relic gravitational waves in cosmic microwave background radiation (CMB). Here, the emphasis is on the temperature-polarization TE cross-correlation function of CMB. The expected numerical level of the correlation, its sign, statistics, and the most appropriate interval of angular scales are identified. Other correlation functions are also considered. The overall conclusion is such that the observational discovery of relic gravitational waves looks like the matter of a few coming years, rather than a few decades.
In the light of the recent results concerning CMB observations and GW detection we address the question of whether it is possible, in a self-consistent inflationary framework, to simultaneously generate a spectrum of scalar metric perturbations in agreement with Planck data and a stochastic background of primordial gravitational radiation compatible with the design sensitivity of aLIGO/Virgo and/or eLISA. We suggest that this is possible in a string cosmology context, for a wide region of the parameter space of the so-called pre-big bang models. We also discuss the associated values of the tensor-to-scalar ratio relevant to the CMB polarization experiments. We conclude that future, cross-correlated results from CMB observations and GW detectors will be able to confirm or disprove pre-big bang models and -- in any case -- will impose new significant constraints on the basic string theory/cosmology parameters.
We present a short review of possible applications of the Wheeler-De Witt equation to cosmological models based on the low-energy string effective action, and characterised by an initial regime of asymptotically flat, low energy, weak coupling evolution. Considering in particular a class of duality-related (but classically disconnected) background solutions, we shall discuss the possibility of quantum transitions between the phases of pre-big bang and post-big bang evolution. We will show that it is possible, in such a context, to represent the birth of our Universe as a quantum process of tunneling or anti-tunneling from an initial state asymptotically approaching the string perturbative vacuum.
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