A Naturally Large Four-Point Function in Single Field Inflation
Leonardo Senatore, Matias Zaldarriaga
TL;DR
This work shows that single-clock inflation can produce a naturally large four-point function as the leading non-Gaussian signal by enforcing an approximate shift symmetry and parity, isolating the quartic operator $\dot{\pi}^4$ and suppressing cubic terms. Using the Effective Field Theory of Inflation, the authors analyze both $\omega \sim c_s k$ and $\omega \sim k^2/M$ dispersion regimes, finding a unique four-point shape in the former and multiple shapes in the latter, with $\tau_{NL}$ potentially well above observational thresholds while $f_{NL}$ remains modest. The results imply that current and future data could detect four-point non-Gaussianities even when three-point signals are weak or absent, motivating dedicated searches in CMB and 21-cm surveys. Overall, the paper identifies a concrete symmetry-protected mechanism for a large four-point signal and maps its observational consequences across different dispersion relations.
Abstract
Non-Gaussianities of the primordial density perturbations have emerged as a very powerful possible signal to test the dynamics that drove the period of inflation. While in general the most sensitive observable is the three-point function in this paper we show that there are technically natural inflationary models where the leading source of non-Gaussianity is the four-point function. Using the recently developed Effective Field Theory of Inflation, we are able to show that it is possible to impose an approximate parity symmetry and an approximate continuos shift symmetry on the inflaton fluctuations that allow, when the dispersion relation is of the form $ω\sim c_s k$, for a unique quartic operator, while approximately forbidding all the cubic ones. The resulting shape for the four-point function is unique. In the models where the dispersion relation is of the form $ω\sim k^2/M$ a similar construction can be carried out and additional shapes are possible.