Title: Cosmic Microwave Background constraints for global strings and global monopoles,
Abstract: We present the first CMB power spectra from numerical simulations of the
global O(N) linear $\sigma$-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 recent 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 monopoles have the same overall shape as those obtained
using the non-linear $\sigma$-model approximation, which is well captured by a
large-N calculation. However, the amplitudes are larger than the large-N
calculation 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 to put limits on the allowed contribution to the temperature power
spectrum at multipole $\ell$ = 10 of 1.7% for global strings and 2.4% for
global monopoles. These limits correspond to symmetry-breaking scales of
2.9x1015 GeV (6.3x1014 GeV with the expected logarithmic scaling of the
effective string tension between the simulation time and decoupling) and
6.4x1015 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 wave from global topological defects will
not be observable at the GW observatory LISA.