Cosmic String Power Spectrum, Bispectrum and Trispectrum

TL;DR

This paper analytically calculates the gravitational effects of cosmic strings on the CMB, focusing on the power spectrum, bispectrum, and trispectrum, especially for upcoming experiments like Planck, revealing distinctive non-Gaussian signatures.

Contribution

It extends previous work by integrating string contributions from last scattering to present, providing new estimates for the bispectrum and trispectrum relevant for CMB observations.

Findings

The bispectrum shape is well-behaved and distinguishable from inflationary signals.

The bispectrum nonlinearity parameter is approximately f_NL  -20.

The trispectrum for cosmic strings is large, with  tau_NL   10^5.

Abstract

We use analytic calculations of the post-recombination gravitational effects of cosmic strings to estimate the resulting CMB power spectrum, bispectrum and trispectrum. We place a particular emphasis on multipole regimes relevant for forthcoming CMB experiments, notably the Planck satellite. These calculations use a flat sky approximation, generalising previous work by integrating string contributions from last scattering to the present day, finding the dominant contributions to the correlators for multipoles l > 50. We find a well-behaved shape for the string bispectrum (without divergences) which is easily distinguishable from the inflationary bispectra which possess significant acoustic peaks. We estimate that the nonlinearity parameter characterising the bispectrum is approximately f_NL \sim -20 (given present string constraints from the CMB power spectrum. We also apply these unequal time correlator methods to calculate the trispectrum for parrallelogram configurations, again valid over a large range of angular scales relevant for WMAP and Planck, as well as on very small angular scales. We find that, unlike the bispectrum which is suppressed by symmetry considerations, the trispectrum for cosmic strings is large. Our current estimate for the trispectrum parameter is tau_NL \sim 10^5, which may provide one of the strongest constraints on the string model as estimators for the trispectrum are developed.