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Published September 15, 2012 | Published + Erratum
Journal Article Open

Probability distribution for non-Gaussianity estimators constructed from the CMB trispectrum


Considerable recent attention has focussed on the prospects to use the cosmic microwave background (CMB) trispectrum to probe the physics of the early universe. Here we evaluate the probability distribution function (PDF) for the standard estimator τ̂_nl for the amplitude τ_nl of the CMB trispectrum both for the null hypothesis (i.e., for Gaussian maps with τnl=0) and for maps with a nonvanishing trispectrum (τ_nl≠0). We find these PDFs to be highly non-Gaussian in both cases. We also evaluate the variance with which the trispectrum amplitude can be measured, ⟨Δτ̂^(2)_(nl)⟩, as a function of its underlying value, τnl. We find a strong dependence of this variance on τ_nl. We also find that the variance does not, given the highly non-Gaussian nature of the PDF, effectively characterize the distribution. Detailed knowledge of these PDFs will therefore be imperative in order to properly interpret the implications of any given trispectrum measurement. For example, if a CMB experiment with a maximum multipole of l_max=1500 (such as the Planck satellite) measures τ̂_nl=0 then at the 95% confidence level our calculations show that we can conclude τ_nl≤1005; assuming a Gaussian PDF but with the correct τnl-dependent variance we would incorrectly conclude τ_nl≤4225; further neglecting the τ_nl-dependence in the variance we would incorrectly conclude τ_nl≤361.

Additional Information

© 2012 American Physical Society. Received 22 June 2012; published 12 September 2012; publisher error corrected 25 September 2012. T. L. S. was supported by the Berkeley Center of Cosmological Physics and thanks the Institute for the Physics and Mathematics of the Universe (IPMU), University of Tokyo, for hospitality while this work was completed. M. K. was supported by DoE Grant No. DE-FG03-92ER40701 and NASA Grant No. NNX12AE86G.

Attached Files

Published - PhysRevD.86.063009.pdf

Erratum - PhysRevD.86.089901.pdf


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