  There are large classes of inflationary models, particularly popular in the
context of string theory and brane world approaches to inflation, in which the
ratio of linearized tensor to scalar metric fluctuations is very small. In such
models, however, gravitational waves produced by scalar modes cannot be
neglected. We derive the lower bound on the tensor-to-scalar ratio by
considering the back-reaction of the scalar perturbations as a source of
gravitational waves. These results show that no cosmological model that is
compatible with a metric scalar amplitude of $\approx 10^{-5}$ can have a ratio
of the tensor to scalar power spectra less than $\approx 10^{-8}$ at
recombination and that higher-order terms leads to logarithmic growth for r
during radiation domination. Our lower bound also applies to non-inflationary
models which produce an almost scale-invariant spectrum of coherent
super-Hubble scale metric fluctuations.
