Angular Trispectrum of CMB Temperature Anisotropy from Primordial Non-Gaussianity with the Full Radiation Transfer Function

Abstract

We calculate the cosmic microwave background (CMB) angular trispectrum, spherical harmonic transform of the four-point correlation function, from primordial non-Gaussianity in primordial curvature perturbations characterized by a constant non-linear coupling parameter, $f_{\mathrm{NL}}$. We fully take into account the effect of the radiation transfer function, and thus provide the most accurate estimate of the signal-to-noise ratio of the angular trispectrum of CMB temperature anisotropy. We find that the predicted signal-to-noise ratio of the trispectrum summed up to a given $l$ is approximately a power-law, $(S/N)(<l)\sim 2.2\times 10^{-9}{f}_{\mathrm{NL}}^2{l}^2$, up to the maximum multipole that we have reached in our numerical calculation, $l=1200$, assuming that the error is dominated by cosmic variance. Our results indicate that the signal-to-noise ratio of the temperature trispectrum exceeds that of the bispectrum at the critical multipole, $l_c\sim 1500(50/|f_{\mathrm{NL}}|)$. Therefore, the trispectrum of the Planck data is more sensitive to primordial non-Gaussianity than the bispectrum for $|f_{\mathrm{NL}}|\gtrsim 50$. We also report the predicted constraints on the amplitude of trispectrum, which may be useful for other non-Gaussian models such as curvaton models.

6 pages, 2 figures, version to be published in PRD

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