Anomalous Dimensions and Non-Gaussianity

TL;DR

This work investigates inflationary signatures from couplings to strongly interacting sectors, focusing on conformal and time-dependent large-N CFTs. By exploiting conformal symmetry and UV-consistent time-dependent flows, it derives how the bispectrum and trispectrum scale in the squeezed and collapsed limits, with exponents fixed by operator dimensions and unitarity. The authors show that a wide variety of shapes—predominantly equilateral or orthogonal, with potential local features—can arise, and that the non-Gaussian amplitude $f_{\rm NL}$ can be substantial for reasonable couplings, providing a precision probe of high-energy physics beyond the inflaton. The results propose concrete observational tests and highlight that higher-dimension operators coupled to inflation may reveal or constrain hidden strongly coupled sectors up to scales $M_*\sim 10^3 H$ and beyond.

Abstract

We analyze the signatures of inflationary models that are coupled to strongly interacting field theories, a basic class of multifield models also motivated by their role in providing dynamically small scales. Near the squeezed limit of the bispectrum, we find a simple scaling behavior determined by operator dimensions, which are constrained by the appropriate unitarity bounds. Specifically, we analyze two simple and calculable classes of examples: conformal field theories (CFTs), and large-N CFTs deformed by relevant time-dependent double-trace operators. Together these two classes of examples exhibit a wide range of scalings and shapes of the bispectrum, including nearly equilateral, orthogonal and local non-Gaussianity in different regimes. Along the way, we compare and contrast the shape and amplitude with previous results on weakly coupled fields coupled to inflation. This signature provides a precision test for strongly coupled sectors coupled to inflation via irrelevant operators suppressed by a high mass scale up to 1000 times the inflationary Hubble scale.

Figures (10)

• Figure 1: The analytic continuation of the contour in conformal time ($\tau$) from Lorentzian signature (blue) to Euclidean signature (red). We calculate the correlation functions for operators at $\tau_0 < 0$. Our expressions involve branch cuts only when ${\rm Re} \tau > 0$, which ensures this continuation is well defined.
• Figure 2: Numerically computed $t(\Delta)$.
• Figure 3: Numerically computed shape function, $S(x_1,x_2)$ evaluated for two values of $\Delta$
• Figure 4: $f_{NL}$ as a function of $\Delta$.
• Figure 5: the shape function for $\Delta=5/4$.