Three-point temperature anisotropies in WMAP: Limits on CMB non-Gaussianities and nonlinearities

2003/05/31 by E. Gaztañaga, E. Gaztanaga, Jeff Wagg +1 · 9 citations
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Galaxies: Formation, Evolution, Phenomena #astro-ph

paper · pdf · doi:10.1103/physrevd.68.021302

published as Phys.Rev. D68 (2003) 021302 · References added. Matches version accepted for publication in Physical Review D

arxiv created 2003/06/12 · openalex publication_date 2003/07/21 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We present a study of the three-point angular correlation function w₃=〈\ensuremathδ₁\ensuremathδ₂\ensuremathδ₃〉 of (adimensional) temperature anisotropies measured by the Wilkinson Microwave Anisotropy Probe. The results can be normalized to the two-point function w₂=〈\ensuremathδ₁\ensuremathδ₂〉 in terms of the hierarchical q₃\ensuremath∼w₃/w₂² or dimensionless d₃\ensuremath∼w₃/w₂^3/2 amplitudes. Strongly non-Gaussian models are generically expected to show d₃>1 or q₃>10³d₃. Unfortunately, this is comparable to the cosmic variance on large angular scales. For Gaussian primordial models, q₃ gives a direct measure of the nonlinear corrections to temperature anisotropies in the sky: \ensuremathδ=\ensuremathδ_L+f_NLT(\ensuremathδ_L²\ensuremath-〈\ensuremathδ_L²〉) with f_NLT=q₃/2 for the leading order term in w₂². We find good agreement with the Gaussian hypothesis d₃\ensuremath∼0 within the cosmic variance of the simulations of the cold dark matter model with a cosmological constant (\ensuremathΛCDM) (with or without a low quadrupole). The strongest constraints on q₃ come from scales smaller than 1\ifmmode^∘\else\textdegree\fi. We find q₃=19\ifmmode±\else\textpm\fi141 for (pseudo) collapsed configurations and an average of q₃=336\ifmmode±\else\textpm\fi218 for noncollapsed triangles. The corresponding nonlinear coupling parameter f_NL for curvature perturbations \ensuremathΦ, in the Sachs-Wolfe regime is f_NL^SW=q₃/6, while on degree scales, the extra power in acoustic oscillations produces f_NL\ensuremath∼q₃/30 in the \ensuremathΛCDM. Errors are dominated by cosmic variance, but for the first time they begin to be small enough to constrain the leading order nonlinear effects with a coupling of the order of unity.

Citations

• Non-Gaussian features of primordial fluctuations in single field inflationary models

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