The most conventional mechanism for gravitational waves (gw) production during inflation is the amplification of vacuum metric fluctuations. In this case the gw production can be uniquely related to the inflationary expansion rate H. For example, a gw detection close to the present experimental limit (tensor-to-scalar ratio r ~ 0.1) would indicate an inflationary expansion rate close to 1014 GeV. This conclusion, however, would be invalid if the observed gw originated from a different source. We construct and study one of the possible covariant formulations of the mechanism suggested in , where a spectator field σ with a sound speed cs Lt 1 acts as a source for gw during inflation. In our formulation σ is described by a so-called P(X) Lagrangian and a non-minimal coupling to gravity. This field interacts only gravitationally with the inflaton, which has a standard action. We compute the amount of scalar and tensor density fluctuations produced by σ and find that, in our realization, r is not enhanced with respect to the standard result but it is strongly sensitive to cs, thus breaking the direct r ↔ H connection.