Optimal analysis of the CMB trispectrum

Abstract

We develop a general framework for data analysis and phenomenology of the CMB four-point function or trispectrum. To lowest order in the derivative expansion, the inflationary action admits three quartic operators consistent with symmetry: ${\dot{\sigma }}^4$, ${\dot{\sigma }}^2(\partial {\sigma }^2)$, and $(\partial \sigma {)}^4$. In single field inflation, only the first of these operators can be the leading non-Gaussian signal. A Fisher matrix analysis shows that there is one near-degeneracy among the three CMB trispectra, so we parameterize the trispectrum with two coefficients $g_{NL}^{{\dot{\sigma }}^4}$ and $g_{NL}^{(\partial \sigma {)}^4}$, in addition to the coefficient $g_{NL}^{\mathrm{loc}}$ of ${\zeta }^3$-type local non-Gaussianity. This three-parameter space is analogous to the parameter space $(f_{NL}^{\mathrm{loc}},f_{NL}^{\mathrm{equil}},f_{NL}^{\mathrm{orth}})$ commonly used to parameterize the CMB three-point function. We next turn to data analysis and show how to represent these trispectra in a factorizable form which leads to computationally fast operations such as evaluating a CMB estimator or simulating a non-Gaussian CMB. We discuss practical issues in CMB analysis pipelines, and perform an optimal analysis of WMAP data. Our minimum-variance estimates are $g_{NL}^{\mathrm{loc}}=(-3.80\pm 2.19)\times 10^5$, $g_{NL}^{{\dot{\sigma }}^4}=(-3.20\pm 3.09)\times 10^6$, and $g_{NL}^{(\partial \sigma {)}^4}=(-10.8\pm 6.33)\times 10^5$ after correcting for the effects of CMB lensing. No evidence of a nonzero inflationary four-point function is seen.

35 pages

Cited by in corpus (16)

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