Back-reaction of gravitational waves revisited

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.