We update constraints on the amplitude of the primordial trispectrum, using the final Planck mission temperature and polarization data. In the squeezed limit, a cosmological local trispectrum would be observed as a spatial modulation of small-scale power on the CMB sky. We reconstruct this signal as a source of statistical anisotropy via quadratic estimator techniques. We systematically demonstrate how the estimated power spectrum of a reconstructed modulation field can be translated into a constraint on τ NL via likelihood methods, demonstrating the procedures effectiveness by inferring known τ NL signal(s) from simulations. Our baseline results constrain τ NL < 1700 at the 95% confidence level, providing the most stringent constraints to date.
We update predictions for observables in the `delicate' D3/D3 inflationary model on the conifold. We use a full CMB likelihood calculation to assess goodness-of-fit, which is necessary because in this model the ζ power spectrum often cannot be approximated as a power-law over observable scales. For the first time we are able to provide accurate forecasts for the amplitude of three-point correlations. In a significant portion of its parameter space the model follows Maldacena's single-field prediction f_NL≈ -(5/12)(ns-1) if |nt| ≪ 1. Therefore |fNL| is usually small when the power spectrum satisfies observational constraints. In a small number of cases the bispectrum is instead dominated by effects from rapid switching between angular minima. The resulting amplitudes are larger, but mostly with unacceptable spectral behaviour. In the most extreme case we obtain |fNL eq| ∼ 75 at kt/3 = 0.002 Mpc-1. It has been suggested that the quasi-single field inflation (`QSFI') mechanism could produce significant 3-point correlations in this model. We do observe rare shifts in amplitude between equilateral and squeezed configurations that could possibly be associated with QSFI effects, but more investigation is needed to establish the full bispectrum shape. There is evidence of `shape' running between equilateral and squeezed configurations that may be inherited from the scale dependence of the spectrum. We explore the dependence of observables on discrete choices such as the truncation point of the potential. Our analysis illustrates the advantages of a standard format for information exchange within the inflationary model-building and testing community.
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