  The production of a stochastic background of relic gravitational waves is
well known in various works in the literature, where, by using the so called
adiabatically-amplified zero-point fluctuations process, it has been shown how
the standard inflationary scenario for the early universe can in principle
provide a distinctive spectrum of relic gravitational waves. In this paper, it
is shown that, in general, f(R) theories of gravity produce a third massive
polarization of gravitational waves and the primordial production of this
polarization is analysed adapting the adiabatically-amplified zero-point
fluctuations process at this case. In this way, previous results, where only
particular cases of f(R) theories have been analysed, will be generalized. The
presence of the mass could also have important applications in cosmology,
because the fact that gravitational waves can have mass could give a
contribution to the dark matter of the Universe. An upper bound for these relic
gravitational waves, which arises from the WMAP constrains, is also released.
At the end of the paper, the potential detection of such massive gravitational
waves using interferometers like Virgo and LIGO is discussed.
