  Primordial gravitational waves (GWs) with frequencies > 10^{-15} Hz
contribute to the radiation density of the Universe at the time of decoupling
of the cosmic microwave background (CMB). The effects of this GW background on
the CMB and matter power spectra are identical to those due to massless
neutrinos, unless the initial density-perturbation amplitude for the
gravitational-wave gas is non-adiabatic, as may occur if such GWs are produced
during inflation or some post-inflation phase transition. In either case,
current observations provide a constraint to the GW amplitude that competes
with that from big-bang nucleosynthesis (BBN), although it extends to much
lower frequencies (~10^{-15} Hz rather than the ~10^{-10} Hz lower limit from
BBN): at 95% confidence-level, Omega_gw h^2 < 6.9 x 10^{-6} for homogeneous
(i.e., non-adiabatic) initial conditions. Future CMB experiments, like Planck
and CMBPol, should allow sensitivities to Omega_gw h^2 < 1.4 x 10^{-6} and
Omega_gw h^2 < 5 x 10^{-7}, respectively.
