On Multifractionality of Spherical Random Fields with Cosmological Applications

TL;DR

This paper explores the multifractional properties of spherical random fields, particularly applied to cosmic microwave background data, revealing spatial variability in regularity and proposing methods for anomaly detection.

Contribution

It introduces a multifractional framework for analyzing CMB data on the sphere and develops new techniques for identifying anomalies in the cosmic microwave background.

Findings

CMB data exhibit multifractionality with location-dependent H"older exponents.

The proposed methods can detect regions with anomalies in CMB maps.

Multifractional analysis provides new insights into the structure of the CMB.

Abstract

This paper studies random fields on the unit sphere. Traditionally, isotropic Gaussian random fields are considered as the underlying statistical model of the cosmic microwave background (CMB) data. This paper discusses the generalized multifractional Brownian motion and its pointwise H\"older 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 obtained results suggest that the estimated H\"older exponents for different CMB regions do change from location to location. Therefore, CMB data are multifractional. Then the developed methodology is used to suggest two approaches for detecting regions with anomalies in cleaned CMB maps.