Abstract
We show that the stochastic background of gravitational waves, produced in the early cosmological epochs, depends strictly on the assumed theory of gravity. In particular, the specific form of the function f(R), where R is the Ricci scalar, is related to the evolution and the production mechanism of gravitational waves. On the other hand, detecting the stochastic background by the forthcoming interferometric experiments (VIRGO, LIGO, LISA) could be a further tool to select the effective theory of gravity.
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