• extended gravity
• gravitational waves
• interferometers

After the First introductory Chapter, where motivations on the extension of General Relativity are discussed from a theoretical point of view and with requirements of phenomenology, the Second Chapter is the ``Core'' of this Ph.D Thesis. In fact, the fundamental goal of this Ph.D Thesis is to compute accurate angular and frequency dependent response functions of interferometers for gravitational waves arising from various Theories of Gravity, i.e. General Relativity and Extended Theories of Gravity. In the case of Extended Theories, both of massless and massive gravitational waves are considered. It has to be recalled that, in the literature which came before the papers founding this Ph.D Thesis, such response functions have been computed, in general, only in the low-frequency approximation. The generalization which is presented has been recently discussed into a part of the scientific community.
In details, Second Chapter is organized in the following way. In Section 2.1 a discussion on the importance of both of the weak-field approximation and the gravitational radiation into the framework of gravity theories is performed. In Section 2.2 the response functions of interferometers to GWs arising from standard General Relativity are computed. In Section 2.3 the discussion is furtherly improved considering the important issue of the ``magnetic'' component of gravitational waves. After this, the case of massless scalar-tensor gravity is considered in Section 2.4. In Section 2.5 the analysis is extended to f(R) theories of gravity.
In the final Section 2.6, a discussion of the presented results is performed, showing that, assuming an improvement in the sensitivity of advanced projects, the presented frequency-dependent response functions could, in principle, help to discriminate between various gravity-theories, while such a potential discrimination will be impossible considering only the low-frequency approximation response functions of previous literature.
In the Third Chapter the analysis is translated in the framework of the most important cosmological source of gravitational radiation, i.e. the stochastic background of relic GWs. Even if such a study could appear ``outside context'', in our personal opinion, the link between Chapter 2 and Chapter 3 is the fact that this Ph.D Thesis has to be considered an analysis of signals and interferometric response functions, and, in a cosmological framework, relic GWs represent the most important signal which could be, in principle, detected.
After a characterization of the ``Standard'' (i.e. which arises from Einstein General Relativity) stochastic background of GWs in Section 3.1, also showing that without the frequency-dependent response functions presented in the Second Chapter the total signal would be overestimated, in Section 3.2 the primordial production of the scalar component arising from massless Scalar Tensor Gravity is analyzed and tuned with the recent WMAP data on Cosmic Background Radiation. After this, in Section 3.3 an analysis on the potential detection of such a scalar component with a cross-correlation between two antennas is performed. Then, in Section 3.4, a specific cross-correlation between the Virgo interferometer and the MiniGRAIL resonant sphere is studied, in the same context of a hypothetical detection of the scalar component and emphasizing that such a potential detection could be important for the viability of Scalar Tensor Gravity.
In the final Section 3.5 we show that a trace of f(R) theories of gravity could be, in principle, present in relic GWs, even if the possibility of detect such a effect is quite difficult.