The trispectrum as a diagnostic of primordial orthogonal non-Gaussianities

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 cs as low as about 0.01, which is actually weakly preferred by WMAP data. For such values, the trispectrum, scaling like 1/c4s, is of order 10 and is therefore comparable to, and greater than, the 1s observational bound teNL = (-3.11 ± 7.5) × 10⁶. 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.