Cosmic strings and domain walls: the impact of CMB $B$-mode data

Abstract

We analyse CMB constraints on stable networks of cosmic strings and domain walls using for the first time full Planck 2018 data together with BICEP/Keck 2018 $B$-mode measurements. The defect-induced anisotropies are computed using the Unconnected Segment Model for Nambu-Goto and Abelian-Higgs strings, as well as for stable domain walls, and included in a full Markov Chain Monte Carlo analysis jointly varying all $Λ$CDM parameters, the tensor-to-scalar ratio, and the string/domain wall tension. No statistically significant evidence for defects is found, although we observe a mild preference for non-zero cosmic string tension. Our results improve previous constraints on the defect power spectrum by up to a factor of two. In the particular case of strings, the improvement is driven by the $B$-mode data, and is especially pronounced for Abelian-Higgs strings. We also present forecasts for upcoming Simons Observatory data and find that, with the baseline noise configuration, the constraints on the string tension could improve by about a factor of three. Finally, we assess the impact of Nambu-Goto string loops on CMB anisotropies in light of both current and future observations.

Figures (12)

• Figure 1: Evolution of the characteristic lengthscale multiplied by the Hubble parameter $LH$ (left panel) and the RMS velocity ${\bar{v}}$ (right panel) as predicted by the VOS models for Nambu-Goto strings (solid blue), Abelian-Higgs strings (solid orange) and domain walls (solid green) in a $\Lambda$CDM background. The dashed lines correspond to the matter-era scaling solutions for each model.
• Figure 2: Left panel: Temperature power spectra, $\mathcal{D}_\ell^{TT} \equiv \ell (\ell + 1) C_\ell^{TT} / (2\pi)$, sourced by NG (orange) and AH (green) string networks, shown together with the $\Lambda$CDM prediction (blue) for reference, computed by fixing the cosmological parameters to values inferred from Planck 2018 data. The string spectra are computed for tensions corresponding to the 95% credible upper limits derived from the Planck$+$BK18 analysis, namely $G\mu = 1.2 \times 10^{-7}$ for NG strings and $G\mu = 1.8 \times 10^{-7}$ for AH strings. Right panel: $B$-mode power spectra, $\mathcal{D}_\ell^{BB} \equiv \ell (\ell + 1) C_\ell^{BB} / (2\pi)$, for the baseline $\Lambda$CDM model (blue), $\Lambda$CDM+$r$ with $r=0.03$ (red), and for $\Lambda$CDM plus NG and AH string networks for the same values of the string tension. We also show the $B$-mode measurements from BICEP/Keck 2018 BICEP:2021xfz for comparison (gray points with error bars).
• Figure 3: Left panel: Temperature power spectra, $\mathcal{D}_\ell^{TT} \equiv \ell (\ell + 1) C_\ell^{TT} / (2\pi)$, for the baseline $\Lambda$CDM model (blue) and for models including a DW network with surface tension $\sigma^{1/3} = 0.81 \; \mathrm{MeV}$ (orange) and $\sigma^{1/3} = 1 \; \mathrm{MeV}$ (green). The latter value corresponds to the original Zel'dovich-Kobzarev-Okun bound Zeldovich:1974uw, while the former represents the 95% credible upper limit derived in this work from a full MCMC analysis (see section \ref{['sec:results']}). The spectra are compared with measurements from the Planck satellite (gray points with error bars) Planck:2019nip. For multipoles $\ell \ge 30$, the data points correspond to the binned Planck 2018 (plik) temperature spectrum. Right panel: $B$-mode power spectra, $\mathcal{D}_\ell^{BB} \equiv \ell (\ell + 1) C_\ell^{BB} / (2\pi)$, for the baseline $\Lambda$CDM model (blue), $\Lambda$CDM+$r$ with $r=0.03$ (green), and for $\Lambda$CDM plus a DW network with surface tension $\sigma^{1/3} = 0.81 \; \mathrm{MeV}$ (orange). The spectra are compared with measurements from BICEP/Keck 2018 (gray points with error bars) BICEP:2021xfz.
• Figure 4: One and two-dimensional posterior distribution functions for $A_{\rm str}$ and the cosmological parameters that exhibit the strongest correlations with the string tension, for NG strings (left) and AH strings (right). The complete triangle plots including all the $\Lambda$CDM parameters are shown in appendix \ref{['appendix:triangle_plots']} (see figures \ref{['fig:Strings_NG_triangle_full']} and \ref{['fig:Strings_AH_triangle_full']}).
• Figure 5: One-dimensional posterior distribution of $A_{\rm DW}$, for different models and dataset combinations.