Gravitational Waves and the Scale of Inflation

We revisit alternative mechanisms of gravitational wave production during inflation and argue that they generically emit a non-negligible amount of scalar fluctuations. We find the scalar power is larger than the tensor power by a factor of order $1/\epsilon^2$. For an appreciable tensor contribution the associated scalar emission completely dominates the zero-point fluctuations of inflaton, resulting in a tensor-to-scalar ratio $r\sim \epsilon^2$. A more quantitative result can be obtained if one further assumes that gravitational waves are emitted by localized sub-horizon processes, giving $r_{\rm max} \simeq 0.3 \epsilon^2$. However, $\epsilon$ is generally time dependent, and this result for $r$ depends on its instantaneous value during the production of the sources, rather than just its average value, somewhat relaxing constraints from the tilt $n_s$. We calculate the scalar 3-point correlation function in the same class of models and show that non-Gaussianity cannot be made arbitrarily small, i.e. $f_{NL} \geq 1$, independently of the value of $r$. Possible exceptions in multi-field scenarios are discussed.