CMB temperature trispectrum of cosmic strings

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 noninteger power-law exponent ‘ with 6< < 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 wave number 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.