Gravitational Waves and the Scale of Inflation

TL;DR

This paper reexamines secondary mechanisms for gravitational-wave production during inflation and demonstrates that energy transfer to an auxiliary sector inevitably sources scalar fluctuations, thereby constraining the tensor-to-scalar ratio. Using energy conservation and the effective field theory of inflation, the authors show that scalar emission generally dominates over tensor emission by a factor of order $1/\epsilon^2$, yielding a robust upper bound $r_{\rm max} \simeq 0.3\epsilon^2$ for sub-horizon, localized sources, with similar limitations in coherent, horizon-scale configurations. They also establish that the associated scalar fluctuations are non-Gaussian, giving $f_{NL} \gtrsim 1$ and a shape close to equilateral/orthogonal, while deriving the scalar and tensor tilt relations $n_s-1 = -\tfrac{1}{2}\epsilon - \tfrac{5}{4}\epsilon_2$ and $n_t = -\tfrac{1}{2}\epsilon + \tfrac{3}{4}\epsilon_2$. The results constrain the scale of inflation in theories with secondary GW production and highlight that observable tensor signals would typically accompany detectable non-Gaussianity, with multifield models offering potential exceptions where the bound can be relaxed or circumvented.

Abstract

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 $1/ε^2$. For an appreciable tensor contribution the associated scalar emission completely dominates the zero-point fluctuations of inflaton, resulting in a tensor-to-scalar ratio $r\sim ε^2$. A more quantitative result can be obtained if one further assumes that gravitational waves are emitted by localized sub-horizon processes, giving $r_{\rm max} \simeq 0.3 ε^2$. However, $ε$ 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.