Abstract
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 cosmic microwave background (CMB) temperature and polarization anisotropies. The radiation field is characterized by four invariants , , , . 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 for , , , 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 correlation at lower ’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 correlation may be a signature more valuable observationally than the lack or presence of the correlation, since the signal is about 100 times stronger than the expected signal. We discuss the detection by WMAP of the anticorrelation at 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 , and correlations.
8 More- Received 18 May 2006
DOI:https://doi.org/10.1103/PhysRevD.74.083008
©2006 American Physical Society