Cosmic microwave background constraints for global strings and global monopoles

Abstract

We present the first cosmic microwave background (CMB) power spectra from numerical simulations of the global O(N) linear σ-model, with N=2,3, which have global strings and monopoles as topological defects. In order to compute the CMB power spectra we compute the unequal time correlators (UETCs) of the energy-momentum tensor, showing that they fall off at high wave number faster than naive estimates based on the geometry of the defects, indicating non-trivial (anti-)correlations between the defects and the surrounding Goldstone boson field. We obtain source functions for Einstein-Boltzmann solvers from the UETCs, using a recently developed method that improves the modelling at the radiation-matter transition. We show that the interpolation function that mimics the transition is similar to other defect models, but not identical, confirming the non-universality of the interpolation function. The CMB power spectra for global strings and global monopoles have the same overall shape as those obtained using the non-linear σ-model approximation, which is well captured by a large-N calculation. However, the amplitudes are larger than the large-N calculation would naively predict, and in the case of global strings much larger: a factor of 20 at the peak. Finally we compare the CMB power spectra with the latest CMB data in other to put limits on the allowed contribution to the temperature power spectrum at multipole l = 10 of 1.7% for global strings and 2.4% for global monopoles. These limits correspond to symmetry-breaking scales of 2.9× 1015 GeV (6.3× 1014 GeV with the expected logarithmic scaling of the effective string tension between the simulation time and decoupling) and 6.4× 1015 GeV respectively. The bound on global strings is a significant one for the ultra-light axion scenario with axion masses ma ≲ 10−28 eV . These upper limits indicate that gravitational waves from global topological defects will not be observable at the gravitational wave observatory LISA.