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Cosmic strings and domain walls: the impact of CMB $B$-mode data
Cosmology and Nongalactic Astrophysics · Submitted 23 Feb 2026 · Published version
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim No statistically significant evidence for defects is found, although we observe a mild preference for non-zero cosmic string tension.
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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 $\Lambda$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 cosmic string power spectrum and correct previous CMB analyses with domain walls that overestimated the constraints. 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 the Simons Observatory and the LiteBIRD satellite: the former will improve string tension constraints by about a factor of three, while the latter those on the domain wall tension by about a factor of five. Finally, we assess the impact of Nambu-Goto string loops on CMB anisotropies in light of both current and future observations.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | 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. | contribution 0.89 | 0.96 | 0.05 | asserted 0.99 |
| s1 | 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 $\Lambda$CDM parameters, the tensor-to-scalar ratio, and the string/domain wall tension. | method 1.00 | 0.94 | 0.03 | asserted 1.00 |
| s2 | No statistically significant evidence for defects is found, although we observe a mild preference for non-zero cosmic string tension. | result 1.00 | 0.97 | 0.80 | asserted 0.98 |
| s3 | Our results improve previous constraints on the cosmic string power spectrum and correct previous CMB analyses with domain walls that overestimated the constraints. | result 0.55 | 0.93 | 0.12 | asserted 1.00 |
| s4 | In the particular case of strings, the improvement is driven by the $B$-mode data, and is especially pronounced for Abelian-Higgs strings. | interpretation 0.77 | 0.92 | 0.07 | asserted 1.00 |
| s5 | We also present forecasts for the Simons Observatory and the LiteBIRD satellite: the former will improve string tension constraints by about a factor of three, while the latter those on the domain wall tension by about a factor of five. | result 0.41 | 0.86 | 0.05 | asserted 0.81 |
| s6 | Finally, we assess the impact of Nambu-Goto string loops on CMB anisotropies in light of both current and future observations. | contribution 0.99 | 0.86 | 0.03 | asserted 0.65 |
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The paper
Original 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 $\Lambda$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 cosmic string power spectrum and correct previous CMB analyses with domain walls that overestimated the constraints. 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 the Simons Observatory and the LiteBIRD satellite: the former will improve string tension constraints by about a factor of three, while the latter those on the domain wall tension by about a factor of five. Finally, we assess the impact of Nambu-Goto string loops on CMB anisotropies in light of both current and future observations.
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References
How the literature uses it
2 arXiv papers cite this in 2 sentences
What it cites · 155 sentences without a confident label
Uses the method or tool of 18 papers
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To include the impact of cosmic string loops on the anisotropies generated from NG string networks, we will follow the approach introduced in [ref] .
CMB anisotropies generated by cosmic string loops · Including cosmic string loops in the USM · 1.00
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The modified Einstein equations in the presence of cosmic strings are implemented in the code [ref] , which computes the CMB spectra generated by string networks based on the phenomenological USM described in the previous sections.
On vector mode contribution to CMB temperature and polarization from local strings · CMB anisotropies in the presence of defect networks · 1.00
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The modified Einstein equations in the presence of cosmic strings are implemented in the code [ref] , which computes the CMB spectra generated by string networks based on the phenomenological USM described in the previous sections.
Cosmic microwave background anisotropy from wiggly strings · CMB anisotropies in the presence of defect networks · 1.00
Uses data or values from 24 papers
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In this work, we have presented an updated and comprehensive analysis of CMB constraints on stable networks of cosmic strings and domain walls, combining the full Planck 2018 temperature and polarization data [ref] with BICEP/Keck 2018 (BK18) $B$-mode measurements [ref] , and extending the analysis with forecasts for the upcoming Simons Observatory (SO) experiment [ref] .
2110.00483 · Conclusions · 0.96
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In this work, we have presented an updated and comprehensive analysis of CMB constraints on stable networks of cosmic strings and domain walls, combining the full Planck 2018 temperature and polarization data [ref] with BICEP/Keck 2018 (BK18) $B$-mode measurements [ref] , and extending the analysis with forecasts for the upcoming Simons Observatory (SO) experiment [ref] .
Planck 2018 results. V. CMB power spectra and likelihoods · Conclusions · 0.96
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In this work, we have presented an updated and comprehensive analysis of CMB constraints on stable networks of cosmic strings and domain walls, combining the full Planck 2018 temperature and polarization data [ref] with BICEP/Keck 2018 (BK18) $B$-mode measurements [ref] , and extending the analysis with forecasts for the upcoming Simons Observatory (SO) experiment [ref] .
The Simons Observatory: Science goals and forecasts · Conclusions · 0.96
Compares with 9 papers
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A NG string network with a tension as high as the best-fit value from Planck$+$BK18, $Gμ=7.8×10^-8$, would generate a Stochastic Gravitational Wave Background (SGWB) with an amplitude in the $n$Hz band that would exceed that of the signal recently reported by pulsar timing experiments [ref] .
The second data release from the European Pulsar Timing Array III. Search for gravitational wave signals · Implications for Gravitational Wave Observatories · 0.88
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A NG string network with a tension as high as the best-fit value from Planck$+$BK18, $Gμ=7.8×10^-8$, would generate a Stochastic Gravitational Wave Background (SGWB) with an amplitude in the $n$Hz band that would exceed that of the signal recently reported by pulsar timing experiments [ref] .
Searching for the nano-Hertz stochastic gravitational wave background with the Chinese Pulsar Timing Array Data Release I · Implications for Gravitational Wave Observatories · 0.88
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A NG string network with a tension as high as the best-fit value from Planck$+$BK18, $Gμ=7.8×10^-8$, would generate a Stochastic Gravitational Wave Background (SGWB) with an amplitude in the $n$Hz band that would exceed that of the signal recently reported by pulsar timing experiments [ref] .
The NANOGrav 15-year Data Set: Evidence for a Gravitational-Wave Background · Implications for Gravitational Wave Observatories · 0.88
Cites as support 3 papers
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Note that we do not include loops in the computation of the anisotropies generated by the AH network because simulations indicate that these loops are short-lived [ref] and thus should not give a significant contribution.
Loop decay in Abelian-Higgs string networks · Including cosmic string loops in the USM · 0.98
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Note that we do not include loops in the computation of the anisotropies generated by the AH network because simulations indicate that these loops are short-lived [ref] and thus should not give a significant contribution.
Nambu-Goto Dynamics of Field Theory Cosmic String Loops · Including cosmic string loops in the USM · 0.98
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Note that we do not include loops in the computation of the anisotropies generated by the AH network because simulations indicate that these loops are short-lived [ref] and thus should not give a significant contribution.
Gravitational wave and particle emission from a cosmic string loop: local case · Including cosmic string loops in the USM · 0.98
Cites as background 8 papers
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We will focus on the gravitational effects of the defects on the CMB, encoded in the unequal-time correlators (UETC) of their stress-energy tensor that act as active sources of perturbations (see also [ref] , for some recent studies exploring non-gravitational probes).
Future CMB constraints on cosmic birefringence and implications for fundamental physics · Introduction · 0.93
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We will focus on the gravitational effects of the defects on the CMB, encoded in the unequal-time correlators (UETC) of their stress-energy tensor that act as active sources of perturbations (see also [ref] , for some recent studies exploring non-gravitational probes).
A CMB Millikan Experiment with Cosmic Axiverse Strings · Introduction · 0.93
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We will focus on the gravitational effects of the defects on the CMB, encoded in the unequal-time correlators (UETC) of their stress-energy tensor that act as active sources of perturbations (see also [ref] , for some recent studies exploring non-gravitational probes).
CMB birefringence from ultra-light axion string networks · Introduction · 0.93
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