Inflationary non-Gaussianities in alpha vacua and consistency with conformal symmetries

Abstract

We study the conformal invariance of inflationary non-Gaussianities associated with scalar fluctuations in a non-Bunch-Davies initial state, known as the alpha-vacuum, in single-field slow-roll inflation. The alpha-vacuum is a one-parameter family of states, including the Bunch-Davies one, that preserves the conformal symmetry of inflationary dynamics in a nearly de-Sitter space-time. Working within the leading slow-roll approximation, we compute the four-point scalar correlator (the trispectrum) in alpha-vacuum using the in-in formalism. We check that the conformal Ward identities are met between the three and four-point scalar alpha-vacua correlators. Surprisingly, this contrasts the previously reported negative result of the Ward identities being violated between the two and the three-point correlators. We have also extended the wave-functional method, previously used for correlators with Bunch-Davies initial condition, to compute the three and four-point scalar correlators in alpha-vacua. The results obtained from the wave-function method match the corresponding in-in results, adding further justification to our check of Ward identities with alpha-vacua correlators.