CMB temperature trispectrum of cosmic strings

TL;DR

This paper derives an analytical expression for the CMB temperature trispectrum caused by cosmic strings, predicting a specific decay pattern and highlighting its dependence on string microstructure and configurations.

Contribution

It provides the first analytical formula for the cosmic string-induced CMB trispectrum, linking it to string properties and exploring various Fourier space configurations.

Findings

Trispectrum decays as l^(-r) with 6<r<7 depending on string microstructure.

The trispectrum can be positive or negative, with strong enhancement in squeezed quadrilaterals.

The model relates the decay exponent to string velocity and loop distribution.

Abstract

We provide an analytical expression for the trispectrum of the Cosmic Microwave Background (CMB) temperature anisotropies induced by cosmic strings. Our result is derived for the small angular scales under the assumption that the temperature anisotropy is induced by the Gott-Kaiser-Stebbins effect. The trispectrum is predicted to decay with a non-integer power-law exponent l^(-r) with 6<r<7, depending on the string microstructure, and thus on the string model. For Nambu-Goto strings, this exponent is related to the string mean square velocity and the loop distribution function. We then explore two classes of wavenumber configuration in Fourier space, the kite and trapezium quadrilaterals. The trispectrum can be of any sign and appears to be strongly enhanced for all squeezed quadrilaterals.