Planck 2013 results. XXV. Searches for cosmic strings and other topological defects

TL;DR

This paper leverages Planck 2013 data to constrain cosmic strings and related topological defects through both power-spectrum and non-Gaussian analyses. It employs dual modelling pipelines, NAMBU USM for Nambu-Goto strings and AH field-theory simulations, alongside semi-local and global texture analyses, to forecast CMB signatures via UETCs and to generate high-resolution defect maps. The study delivers stringent upper bounds on the string tension across several models, with Planck+WP+highL tightening Gμ/c^2 to about 1–4×10^{-7} depending on the defect type, and f10 constrained to the low-percent range; non-Gaussian tests (bispectrum, steerable wavelets, Minkowski functionals) provide independent limits around 7–9×10^{-7}, validating the power-spectrum results. Collectively, the results place tight constraints on theories predicting GUT-scale defects and underscore Planck’s capability to probe fundamental physics with both linear and non-Gaussian CMB imprints.

Abstract

Planck data have been used to provide stringent new constraints on cosmic strings and other defects. We describe forecasts of the CMB power spectrum induced by cosmic strings, calculating these from network models and simulations using line-of-sight Boltzmann solvers. We have studied Nambu-Goto cosmic strings, as well as field theory strings for which radiative effects are important, thus spanning the range of theoretical uncertainty in strings models. We have added the angular power spectrum from strings to that for a simple adiabatic model, with the extra fraction defined as $f_{10}$ at multipole $\ell=10$. This parameter has been added to the standard six parameter fit using COSMOMC with flat priors. For the Nambu-Goto string model, we have obtained a constraint on the string tension of $Gμ/c^2 < 1.5 x 10^{-7}$ and $f_{10} < 0.015$ at 95% confidence that can be improved to $Gμ/c^2 < 1.3 x 10^{-7}$ and $f_{10} < 0.010$ on inclusion of high-$\ell$ CMB data. For the abelian-Higgs field theory model we find, $Gμ_{AH}/c^2 < 3.2 x 10^{-7}$ and $f_{10} < 0.028$. The marginalized likelihoods for $f_{10}$ and in the $f_{10}$--$Ω_b h^2$ plane are also presented. We have also obtained constraints on $f_{10}$ for models with semi-local strings and global textures for which $Gμ/c^2 < 1.1 x 10^{-6}$. We have made complementarity searches for the specific non-Gaussian signatures of cosmic strings, calibrating with all-sky Planck resolution CMB maps generated from networks of post-recombination strings. We have obtained upper limits on the string tension at 95% confidence of $Gμ/c^2 < 8.8 x 10^{-7}$ using modal bispectrum estimation and $Gμ/c^2 < 7.8 x 10^{-7}$ for real space searches with Minkowski functionals. These are conservative upper bounds because only post-recombination string contributions have been included in the non-Gaussian analysis.

Figures (14)

• Figure 1: The spacetime around a cosmic string is conical, as if a narrow wedge were removed from a flat sheet and the edges identified. For this reason cosmic strings can create double images of distant objects. Strings moving across the line of sight will cause line-like discontinuities in the CMB radiation.
• Figure 2: Characteristic CMB temperature discontinuity created by a cosmic string. Here, the simulated Nambu-Goto string has produced a cusp, a small region on the string that approaches the speed of light, which has generated a localised CMB signal.
• Figure 3: Cosmic string power spectra used in this analysis: NAMBU (black dashed), AH-mimic (blue dotted) and AH (red solid). The spectra have been normalized to equal power at $\ell=10$. The spectra are normalized the observed WMAP7 value at $\ell=10$ and have $G\mu/c^2=1.17\times 10^{-6}$, $1.89\times 10^{-6}$ and $2.04\times 10^{-6}$ respectively. Note that the limits discussed in this paper mean that the CMB spectra presented here are less than $3\%$ of the overall power spectrum amplitude and hence the differences observed at high $\ell$ do not have a much effect.
• Figure 4: Comparison between global texture (black dashed) and semilocal (blue dotted) string power spectra and the AH field theory strings (red solid), normalized to unity at $\ell=10$. As expected, the SL spectrum lies in between the TX and the AH spectra. The AH spectrum was recomputed for the Planck cosmological model with sources from Bevis:2010gj, and the SL and TX spectra were taken from Urrestilla:2007sf.
• Figure 5: Integrated Sachs-Wolfe angular power spectra extracted from the full sky cosmic string maps at different resolutions (labelled by $N_\mathrm{side}$), with or without applying the anti-aliasing procedure (see text). The anti-aliasing filtering gives back the correct power up to $\ell_{\max} \lesssim 2 N_\mathrm{side}$.