  The relic gravitational wave background due to tensor linear perturbations
generated during Higgs inflation is computed. Both the Standard Model and a
well-motivated phenomenological completion (that accounts for all the
experimentally confirmed evidence of new physics) are considered. We focus on
critical Higgs inflation, which improves on the non-critical version and
features an amplification of the tensor fluctuations. The latter property
allows us to establish that future space-borne interferometers, such as DECIGO,
BBO and ALIA, may detect the corresponding primordial gravitational waves.
