# 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 powermore »

- Authors:

- Department of Theoretical Physics, University of the Basque Country UPV/EHU, 48080 Bilbao (Spain)
- Department of Physics and Astronomy, University of Sussex, Brighton, BN1 9QH (United Kingdom)

- Publication Date:

- OSTI Identifier:
- 22676101

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Cosmology and Astroparticle Physics; Journal Volume: 2017; Journal Issue: 07; Other Information: Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; 79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; AMPLITUDES; APPROXIMATIONS; AXIONS; COMPARATIVE EVALUATIONS; COMPUTERIZED SIMULATION; DECOUPLING; ENERGY-MOMENTUM TENSOR; GEV RANGE; GRAVITATIONAL WAVES; INTERPOLATION; MASS; MONOPOLES; MULTIPOLES; NONLINEAR PROBLEMS; RELICT RADIATION; SIGMA MODEL; SPECTRA; SYMMETRY BREAKING

### Citation Formats

```
Lopez-Eiguren, Asier, Lizarraga, Joanes, Urrestilla, Jon, and Hindmarsh, Mark, E-mail: asier.lopez@ehu.eus, E-mail: joanes.lizarraga@ehu.eus, E-mail: m.b.hindmarsh@sussex.ac.uk, E-mail: jon.urrestilla@ehu.eus.
```*Cosmic microwave background constraints for global strings and global monopoles*. United States: N. p., 2017.
Web. doi:10.1088/1475-7516/2017/07/026.

```
Lopez-Eiguren, Asier, Lizarraga, Joanes, Urrestilla, Jon, & Hindmarsh, Mark, E-mail: asier.lopez@ehu.eus, E-mail: joanes.lizarraga@ehu.eus, E-mail: m.b.hindmarsh@sussex.ac.uk, E-mail: jon.urrestilla@ehu.eus.
```*Cosmic microwave background constraints for global strings and global monopoles*. United States. doi:10.1088/1475-7516/2017/07/026.

```
Lopez-Eiguren, Asier, Lizarraga, Joanes, Urrestilla, Jon, and Hindmarsh, Mark, E-mail: asier.lopez@ehu.eus, E-mail: joanes.lizarraga@ehu.eus, E-mail: m.b.hindmarsh@sussex.ac.uk, E-mail: jon.urrestilla@ehu.eus. Sat .
"Cosmic microwave background constraints for global strings and global monopoles". United States.
doi:10.1088/1475-7516/2017/07/026.
```

```
@article{osti_22676101,
```

title = {Cosmic microwave background constraints for global strings and global monopoles},

author = {Lopez-Eiguren, Asier and Lizarraga, Joanes and Urrestilla, Jon and Hindmarsh, Mark, E-mail: asier.lopez@ehu.eus, E-mail: joanes.lizarraga@ehu.eus, E-mail: m.b.hindmarsh@sussex.ac.uk, E-mail: jon.urrestilla@ehu.eus},

abstractNote = {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× 10{sup 15} GeV (6.3× 10{sup 14} GeV with the expected logarithmic scaling of the effective string tension between the simulation time and decoupling) and 6.4× 10{sup 15} GeV respectively. The bound on global strings is a significant one for the ultra-light axion scenario with axion masses m {sub a} ∼< 10{sup −28} eV . These upper limits indicate that gravitational waves from global topological defects will not be observable at the gravitational wave observatory LISA.},

doi = {10.1088/1475-7516/2017/07/026},

journal = {Journal of Cosmology and Astroparticle Physics},

number = 07,

volume = 2017,

place = {United States},

year = {Sat Jul 01 00:00:00 EDT 2017},

month = {Sat Jul 01 00:00:00 EDT 2017}

}