This paper is a review of previous works on the stochastic background of gravitational waves (SBGWs) whichhas been discussed in various peer-reviewed journals and international conferences. The SBGWs is analyzed with the aidof the Wilkinson Microwave Anisotropy Probe (WMAP) data. We emphasize that, in general, in previous works in theliterature about the SBGWs, old Cosmic Background Explorer (COBE) data were used. After this, we want to face theproblem of how the SBGWs and ?(R) gravity (where ?(R) is a function of the Ricci scalar R) can be related, showing, viceversa, that a revealed SBGWs could be a powerful probe for a given theory of gravity. In this way, it will also be shownthat the conform treatment of SBGWs can be used to parameterize in a natural way ?(R) theories. Some interestingexamples which have been recently discussed in the literature will be also analysed. The presence and the potential detection of the SBGWs is quite important in the framework of the debate on high-frequency gravitational waves (HFGWs) too. Recently, the importance of HFGWs has been emphasized in some papers inthe literature.
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