The Trispectrum as a Diagnostic of Primordial Orthogonal non-Gaussianities

TL;DR

This paper investigates how the trispectrum can serve as a powerful diagnostic tool for detecting primordial orthogonal non-Gaussianities in single-field inflation models with low sound speed, potentially constraining inflationary theories.

Contribution

It demonstrates that the trispectrum, scaling as 1/c_s^4, can constrain inflation models with orthogonal bispectra, especially with upcoming Planck data, highlighting the importance of trispectrum analysis.

Findings

Trispectrum amplitude can reach 10^8 for low sound speeds.

Current observational bounds already constrain some inflation models.

Future Planck data could significantly restrict the parameter space.

Abstract

In single-field inflationary models with a low sound speed, the orthogonal shape of the primordial bispectrum arises due to partial cancellations between equilateral-type shapes. This fact allows for a speed of sound c_s as low as about 0.01, which is actually weakly preferred by WMAP data. For such values, the trispectrum, scaling like 1/c_s^4, is of order 10^8 and is therefore comparable to, and greater than, the 1 sigma observational bound t_NL^eq=(-3.11 +- 7.5)*10^6. Hence, the trispectrum is already constraining inflationary mechanisms candidates for generating an orthogonal bispectrum at the level hinted in WMAP data. If this signal persists in imminent Planck data, most of the parameter space of the simplest effective field theory of inflation will be under observational pressure, while a dedicated analysis will be needed for the substantial fraction of parameter space where we show that a qualitatively new, orthogonal, trispectrum naturally arises.