On multifractionality of spherical random fields with cosmological applications

Authors

DOI:

https://doi.org/10.21914/anziamj.v64.16742

Keywords:

random fields, multifractionality, Hölder exponent, spherical statistics, cosmic microwave background , radiation, CMB anomalies

Abstract

This paper investigates spatial data on the unit sphere. Traditionally, isotropic Gaussian random fields are considered as the underlying mathematical model of the cosmic microwave background (CMB) data. We discuss the generalized multifractional Brownian motion and its pointwise Hölder exponent on the sphere. The multifractional approach is used to investigate the CMB data from the Planck mission. These data consist of CMB radiation measurements at narrow angles of the sky sphere. The results obtained suggest that the estimated Hölder exponents for different CMB regions do change from location to location. Therefore, the CMB temperature intensities are multifractional. The methodology developed is used to suggest two approaches for detecting regions with anomalies in the cleaned CMB maps.

doi:10.1017/S1446181122000104

 

Author Biographies

Philip Broadbridge, La Trobe University

Department of Mathematics and Statistics, La Trobe University, Melbourne, VIC Australia.

Ravindi Nanayakkara, La Trobe University

Department of Mathematics and Statistics, La Trobe University, Melbourne, VIC Australia.

Andriy Olenko, La Trobe University

Department of Mathematics and Statistics, La Trobe University, Melbourne, VIC Australia.

Published

2022-08-28

Issue

Section

Articles for Printed Issues