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Abstract: We present trispectrum estimation methods which can be applied to generalnon-separable primordial and CMB trispectra. We present a general optimalestimator for the connected part of the trispectrum, for which we derive aquadratic term to incorporate the effects of inhomogeneous noise and masking.We describe a general algorithm for creating simulated maps with givenarbitrary and independent power spectra, bispectra and trispectra. We proposea universal definition of the trispectrum parameter $T {NL}$, so that theintegrated bispectrum on the observational domain can be consistently comparedbetween theoretical models. We define a shape function for the primordialtrispectrum, together with a shape correlator and a useful parametrisation forvisualizing the trispectrum. We derive separable analytic CMB solutions in thelarge-angle limit for constant and local models. We present separable modedecompositions which can be used to describe any primordial or CMB bispectra ontheir respective wavenumber or multipole domains. By extracting coefficients ofthese separable basis functions from an observational map, we are able topresent an efficient estimator for any given theoretical model with anonseparable trispectrum. The estimator has two manifestations, comparing thetheoretical and observed coefficients at either primordial or late times. Thesemode decomposition methods are numerically tractable with order $l^5$operations for the CMB estimator and approximately order $l^6$ for the generalprimordial estimator reducing to order $l^3$ in both cases for a special classof models. We also demonstrate how the trispectrum can be reconstructed fromobservational maps using these methods.



Author: D.M. Regan, E.P.S. Shellard, J.R. Fergusson

Source: https://arxiv.org/



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