Cosmological matching conditions for gravitational waves at second order
  We compute the second-order matching conditions for tensor metric
perturbations at an abrupt change in the equation of state. For adiabatic
perturbations on large scales the matching hypersurface coincides with a
uniform-density hypersurface. We show that in the uniform-density gauge both
the tensor perturbation and its time-derivative are continuous in this case.
For non-adiabatic perturbations, the matching hypersurface need not coincide
with a uniform-density hypersurface and the tensor perturbation in the
uniform-density gauge may be discontinuous. However, we show that in the
Poisson gauge both the tensor perturbation and its time-derivative are
continuous for adiabatic or non-adiabatic perturbations. As an application we
solve the evolution equation for second-order tensor perturbations on large
scales for a constant equation of state and we use the matching conditions to
evolve the solutions through the transition from an inflationary era to a
radiation era. We show that in the radiation era the resulting free part of the
large-scale tensor perturbation (constant mode) is slow-roll suppressed in both
the uniform-density and Poisson gauges. Thus, we conclude that second-order
gravitational waves from slow-roll inflation are suppressed.
