  The production of a stochastic background of relic gravitational waves is
well known in various works in the literature, where, 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 a weak modification of General Relativity produces 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. The presence of the mass could also have
important applications in cosmology as the fact that gravitational waves can
have mass could give a contribution to the dark matter of the Universe. At the
end of the paper an upper bound for these relic gravitational waves, which
arises from the WMAP constrains, is also released.
