Consistency relations for sharp features in the primordial spectra

Abstract

We study the generation of sharp features in the primordial spectra within\nthe framework of effective field theory of inflation, wherein curvature\nperturbations are the consequence of the dynamics of a single scalar degree of\nfreedom. We identify two sources in the generation of features: rapid\nvariations of the sound speed c_s (at which curvature fluctuations propagate)\nand rapid variations of the expansion rate H during inflation. With this in\nmind, we propose a non-trivial relation linking these two quantities that\nallows us to study the generation of sharp features in realistic scenarios\nwhere features are the result of the simultaneous occurrence of these two\nsources. This relation depends on a single parameter with a value determined by\nthe particular model (and its numerical input) responsible for the rapidly\nvarying background. As a consequence, we find a one-parameter consistency\nrelation between the shape and size of features in the bispectrum and features\nin the power spectrum. To substantiate this result, we discuss several examples\nof models for which this one-parameter relation (between c_s and H) holds,\nincluding models in which features in the spectra are both sudden and resonant.\n