  We study the back-reaction of gravitational waves in early universe
cosmology, focusing both on super-Hubble and sub-Hubble modes. Sub-Hubble modes
lead to an effective energy density which scales as radiation. Hence, the
relative contribution of such gravitational waves to the total energy density
is constrained by big bang nucleosynthesis. This leads to an upper bound on the
tensor spectral slope n_T which also depends on the tensor to scalar ratio r.
Super-Hubble modes, on the other hand, lead to a negative contribution to the
effective energy density, and to an equation of state of curvature. Demanding
that the early universe is not dominated by the back-reaction leads to
constraints on the gravitational wave spectral parameters which are derived.
