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.
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