Astronomy and Astrophysics – Astrophysics – Cosmology and Extragalactic Astrophysics
Scientific paper
2011-04-05
Astronomy and Astrophysics
Astrophysics
Cosmology and Extragalactic Astrophysics
10 pages, 6 figures, comments welcome
Scientific paper
One of the principle efforts in cosmic microwave background (CMB) research is measurement of the parameter fnl that quantifies the departure from Gaussianity in a large class of non-minimal inflationary (and other) models. Estimators for fnl are composed of a sum of products of the temperatures in three different pixels in the CMB map. Since the number ~Npix^2 of terms in this sum exceeds the number Npix of measurements, these ~Npix^2 terms cannot be statistically independent. Therefore, the central-limit theorem does not necessarily apply, and the probability distribution function (PDF) for the fnl estimator does not necessarily approach a Gaussian distribution for N_pix >> 1. Although the variance of the estimators is known, the significance of a measurement of fnl depends on knowledge of the full shape of its PDF. Here we use Monte Carlo realizations of CMB maps to determine the PDF for two minimum-variance estimators: the standard estimator, constructed under the null hypothesis (fnl=0), and an improved estimator with a smaller variance for |fnl| > 0. While the PDF for the null-hypothesis estimator is very nearly Gaussian when the true value of fnl is zero, the PDF becomes significantly non-Gaussian when |fnl| > 0. In this case we find that the PDF for the null-hypothesis estimator fnl_hat is skewed, with a long non-Gaussian tail at fnl_hat > |fnl| and less probability at fnl_hat < |fnl| than in the Gaussian case. We provide an analytic fit to these PDFs. On the other hand, we find that the PDF for the improved estimator is nearly Gaussian for observationally allowed values of fnl. We discuss briefly the implications for trispectrum (and other higher-order correlation) estimators.
Kamionkowski Marc
Smith Tristan L.
Wandelt Benjamin D.
No associations
LandOfFree
The Probability Distribution for Non-Gaussianity Estimators does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with The Probability Distribution for Non-Gaussianity Estimators, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The Probability Distribution for Non-Gaussianity Estimators will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-416470