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A Measurement of Cubic-Order Primordial Non-Gaussianity (g_{NL} and τ_{NL}) With WMAP 5-Year Data

Joseph Smidt, Alexandre Amblard, Asantha Cooray, Alan Heavens, Dipak Munshi, Paolo Serra

Abstract

We measure two higher-order power spectra involving weighted cubic and squared temperature anisotropy maps from WMAP 5-year data to study the trispectrum generated by primordial non-Gaussianity. Using these measurements combined with Gaussian and noise simulations, we constrain the cubic order non-Gaussianity parameters τ_{NL}, and g_{NL}. With V+W-band data out to l_{max}=600, we find -7.4 < g_{\rm NL}/10^5 < 8.2 and -0.6 < τ_{\rm NL}/10^4 < 3.3 improving the previous COBE-based limit on τ_{\rm NL} < 10^8 nearly four orders of magnitude with WMAP. We find that the ratio of trispectrum to bispectrum amplitude as captured by the ratio of τ_{\rm Nl}/(6f_{\rm NL}/5)^2 ranges from -3 to 21 at the 95% confidence level.

A Measurement of Cubic-Order Primordial Non-Gaussianity (g_{NL} and τ_{NL}) With WMAP 5-Year Data

Abstract

We measure two higher-order power spectra involving weighted cubic and squared temperature anisotropy maps from WMAP 5-year data to study the trispectrum generated by primordial non-Gaussianity. Using these measurements combined with Gaussian and noise simulations, we constrain the cubic order non-Gaussianity parameters τ_{NL}, and g_{NL}. With V+W-band data out to l_{max}=600, we find -7.4 < g_{\rm NL}/10^5 < 8.2 and -0.6 < τ_{\rm NL}/10^4 < 3.3 improving the previous COBE-based limit on τ_{\rm NL} < 10^8 nearly four orders of magnitude with WMAP. We find that the ratio of trispectrum to bispectrum amplitude as captured by the ratio of τ_{\rm Nl}/(6f_{\rm NL}/5)^2 ranges from -3 to 21 at the 95% confidence level.

Paper Structure

This paper contains 6 equations, 3 figures, 1 table.

Figures (3)

  • Figure 1: The top plot shows the ${\cal K}_l^{3,1}$ and ${\cal K}_l^{2,2}$ estimators, shown in green and blue respectively, taken from data for the W band. The same estimators for the V band are shown on the bottom. Additionally on the top the theoretical contributions for ${\cal K}_l^{2,2}$ and ${\cal K}_l^{3,1}$ proportional to $\tau_{\rm NL}$ are shown with the bottom showing those proportional to $g_{\rm NL}$. The Gaussian contributions were not removed from these plots.
  • Figure 2: The relation between the full estimators coming from data versus the Gaussian contributions. The green curve show the Gaussian contributions coming from averaging the estimators from the Gaussian maps. The red curve is the theoretical Gaussian piece calculated from Eq. \ref{['eq:gausspiece']} using the WMAP-5 best-fit cosmology power spectrum. The error bars show two standard deviations from the Gaussian curves. These curves are from W band data.
  • Figure 3: The 95% confidence levels for $g_{\rm NL}$ versus $\tau_{\rm NL}$. The red and orange represent the 68% and 95% intervals respectively for the combined V+W analysis. The light blue regions represent the 95% confidence intervals for the V band analysis, and the light green regions are for the W band.