Galilean symmetry in the effective theory of inflation: new shapes of non-Gaussianity

TL;DR

This work investigates single-field inflation with an approximate Galilean symmetry, focusing on an EFT for perturbations described by the π field. By restricting to Galilean-invariant operators with at least two derivatives per field and using the decoupling limit, the authors derive a cubic action containing three independent operators, leading to two equilateral-like and one flattened non-Gaussian bispectrum shapes, and a potentially enhanced four-point function. They quantify the observable templates for these shapes, showing strong overlaps with equilateral and enfolded templates for two operators while identifying a third shape that is nearly orthogonal to standard templates, motivating dedicated data analyses. The study also highlights that the four-point signal can be sizable in this framework, offering a promising avenue to test Galilean EFTs with Planck data and future observations. These results broaden the landscape of inflationary non-Gaussianity and motivate further exploration of higher-derivative Galilean operators and multi-field extensions.

Abstract

We study the consequences of imposing an approximate Galilean symmetry on the Effective Theory of Inflation, the theory of small perturbations around the inflationary background. This approach allows us to study the effect of operators with two derivatives on each field, which can be the leading interactions due to non-renormalization properties of the Galilean Lagrangian. In this case cubic non-Gaussianities are given by three independent operators, containing up to six derivatives, two with a shape close to equilateral and one peaking on flattened isosceles triangles. The four-point function is larger than in models with small speed of sound and potentially observable with the Planck satellite.

Figures (3)

• Figure 1: Bispectrum shapes generated by the cubic operators in Eq. \ref{['eq:Sint']}. The ones proportional to $M_1$ and $M_2$ (upper panels) are very similar (with a cosine of nearly 1) to those generated by $\dot\pi^3$ and $\dot\pi(\partial_i\pi)^2$ respectively, which where studied in Alishahiha:2004ehChen:2006ntCheung:2007st. They have a cosine of 0.96 and 0.99 with the equilateral template. The third operator (lower left panel) is "surfing", i.e. it is shaped like a wave with a maximum in the flat configuration, and has a large overlap with the enfolded template (lower right panel). The suppression in the equilateral regime is due to the presence of a higher number of scalar products of gradients.
• Figure 2: Left: regions of the parameter space $M_2/M_1$ and $M_3/M_1$ for which the cosine of the resulting shape with the local, equilateral and orthogonal template is smaller than 0.2. Right: Non-Gaussian shape obtained with $M_2=0.32 M_1$ and $M_3=-0.42 M_1$. This shape is nearly orthogonal to all known templates (with cosines of -0.15, 0.03, 0.06 and -0.03 with the local, equilateral, orthogonal and enfolded template), and would require a dedicated template for data analysis.
• Figure 3: In the left panel this figure we show the template \ref{['app:eq:template']} that goes to zero in the squeezed limit and has a large cosine with the physical bispectrum shape generated by the operator proportional to $M_3$, which is shown in the right panel for comparison.