Vanishing of local non-Gaussianity in canonical single field inflation

Abstract

We study the production of observable primordial local non-Gaussianity in two opposite regimes of canonical single field inflation: attractor (standard single field slow-roll inflation) and non attractor (ultra slow-roll inflation). In the attractor regime, the standard derivation of the bispectrum's squeezed limit using co-moving coordinates gives the well known Maldacena's consistency relation fNL = 5 (1−ns) / 12. On the other hand, in the non-attractor regime, the squeezed limit offers a substantial violation of this relation given by fNL = 5/2. In this work we argue that, independently of whether inflation is attractor or non-attractor, the size of the observable primordial local non-Gaussianity is predicted to be fNLobs = 0 (a result that was already understood to hold in the case of attractor models). To show this, we follow the use of the so-called Conformal Fermi Coordinates (CFC), recently introduced in the literature. These coordinates parametrize the local environment of inertial observers in a perturbed FRW spacetime, allowing one to identify and compute gauge invariant quantities, such as n-point correlation functions. Concretely, we find that during inflation, after all the modes have exited the horizon, the squeezed limit of the 3-point correlation function of curvature perturbations vanishes in the CFC frame, regardless of the inflationary regime. We argue that such a cancellation should persist after inflation ends.

Soft theorems for shift-symmetric cosmologies

“…B. F., G. G., and E. P. are supported by the Delta-ITP Note added.-While finishing this paper, we became aware that [20] was also completing related work. Both our works were submitted to the arXiv on the same day, but due to an unfortunate typographical error in one of the iterations of "shift symmetry" our paper was put on hold and appeared only two days later.…”

Steepest growth of the power spectrum and primordial black holes

“…However, Cai et al have recently shown that ending USR with a smooth transition tends to erase the local non-Gaussianity [74]. If the local non-Gaussianity is not erased or modified by the way USR ends, it has a value f NL = 5/2 for modes which exited the horizon long after USR begins (see [75,76] for coordinate-choice issues). f NL ∼ 1 was shown to have a significant impact on the power spectrum constraints in [77], while the higher-order non-linearity parameters and mode coupling are also important [78][79][80].…”

The Hunt for Primordial Interactions in the Large-Scale Structures of the Universe

“…This non-Gaussianity can be connected to a local-type one by an appropriate matching [47], so that one would be tempted to state that we are expected to see a minimal amount of non-Gaussianity in the scale dependent bias. However, following an interesting debate [53, [233][234][235][236][237][238][239]267,268], it has been shown that the single-field consistency relation is equivalent to the statement that long-wavelength perturbations are not physically coupled to small-scale ones and therefore there is no scale-dependent bias for single-field models of inflation. The argument follows from studying how to connect the result of [47], which was computed in comoving gauge at the epoch of inflation, with actual observations of galaxy number counts at the present day.…”