The trispectrum as a diagnostic of primordial orthogonal non-Gaussianities

Abstract

Abstract. In single-field inflationary models with a low sound speed, the orthogonal shape of the primordial bispectrum arises due to partial cancellations between equilateraltype 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 4 s , is of order 10 8 and is therefore comparable to, and greater than, the 1σ observational bound t eq N L = (−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.

On the trispectrum of Galileon inflation

“…In what follows we will neglect metric perturbations, this is because we will work in the decoupling limit [37]. The latter is completely analogous to what happens within the effective theory approach to inflation of [68] (see also [69][70][71][72][73]): there the large non linearities of the pseudo-goldstone boson π win over the mixed π-metric perturbations above a certain energy regime E mix 4 . This scale E mix must be paired with the scale Λ of the underlying theory when identifying the regime of validity for the effective field theory.…”

DBI Galileon in the effective field theory of inflation: orthogonal non-Gaussianities and constraints from the Trispectrum

“…Unless inflation occurred in the region of parameter space where similar competitions that leads to the orthogonal bispectrum arise at the level of the trispectrum, the amplitude of the latter, scaling as 1/c 4 s , is of order 10 8 and hence is comparable to (and greater than) current observational constraint t eq N L = (−3.11 ± 7.5) × 10 6 [39]. DBI Galileon inflation does not belong to the simple of class of models in which we quantitatively developed this argument in [25], and the results derived there can not be simply applied here. Yet, we have seen that the two frameworks share similar qualitative features and it is therefore reasonable to expect similar constraints on this model from the trispectrum.…”

“…Our second aim is to investigate the possibility of observationally falsifying DBI Galileon inflation as an inflationary scenario candidate for explaining the large orthogonal bispectrum suggested in WMAP data [21]. Indeed, we recently pointed out the fact that the trispectrum can be used, already with current data, to constrain such candidates in the simplest theoretical framework [25]. Although the two setups are different, we will see that similar conclusions can also be reached here, and that the trispectrum is putting the DBI Galileon model under strong observational pressure, at least in the 1σ region favored by WMAP9 constraints on the bispectrum.…”

“…Fortunately, we have checked this to be the case in the interesting region α 0.095 favored (at 2σ) by the observational constraints on the bispectrum (see figure 2 in the preceding subsection). 7 For this purpose, we used the same strategy as in [25] and represented 2-dimensional slices of our trispectrum (3.33) (as a function of α) in different representative limits, as was originally done in [37]. We display the outcome of this procedure for the representative value α = 0.097 (in the middle of the 1σ region favored by the bispectrum) in appendix C, from which the approximate proportionality with T c1 is manifest.…”

Halo/galaxy bispectrum with equilateral-type primordial trispectrum

“…Finally, as is mentioned above, we have concentrated on three equilateral-type primordial trispectra whose amplitudes are constrained by CMB observations and theoretical origin is very clear. But there are still many interesting primordial trispectra generated by theoretical models which produce the equilateral-type bispectrum [45][46][47][48][49][50][51][52][53][54][55][56][57][58][59]. Although constraints are not obtained for these trispectra even by CMB observations, it might be interesting to consider the possibility to constrain these primordial trispectra based on the large scale halo/galaxy distributions.…”