Search for Cosmic Strings in CMB Anisotropies

TL;DR

The paper searches for cosmic strings in the CMB using the WMAP 1-year W-band map, addressing whether string-induced non-Gaussian features or temperature steps are detectable. It develops a quadratic-variance bound and a pattern-search algorithm to constrain the deficit angle $\delta = 8\pi G\mu / c^2$, yielding upper limits of $\delta < 0.82\times10^{-5}$ (variance) and $\delta < 1.54\times10^{-5}$ (pattern search), with a weaker bound $\delta < 7.34\times10^{-5}$ under a uniform distribution model. These limits translate to symmetry-breaking scales around $\eta_{SB} \sim$ a few $\times 10^{16}$ GeV, and no compelling string signature is found in the data. The work demonstrates a concrete pattern-search framework for identifying string-like features in CMB maps, offering a pathway for tighter constraints with future data.

Abstract

We have searched the 1st-year WMAP W-Band CMB anisotropy map for evidence of cosmic strings. We have set a limit of $δ= 8 πG μ/ c^2 < 8.2 \times 10^{-6}$ at 95% CL for statistical search for a significant number of strings in the map. We also have set a limit using the uniform distribution of strings model in the WMAP data with $δ= 8 πG μ/ c^2 < 7.34 \times 10^{-5}$ at 95% CL. And the pattern search technique we developed here set a limit $δ= 8 πG μ/ c^2 < 1.54 \times 10^{-5}$ at 95% CL.

Figures (10)

• Figure 1: Probability distributions for temperature steps in equation (\ref{['b']}). The solid curve represents the probability with both string direction $\hat{s}$ and string velocity $\vec{\beta}$ having random directions while the flat dotted line assumes $\hat{\beta} \bot \hat{s}$ ($\sin\phi =1$) but the direction of $\hat{\beta} \times \hat{s}$ is random relative to the line of sight ($\cos\theta$ random).
• Figure 2: Temperature Distribution of full sky from WMAP. Pixels with $|\Delta T| > 1mK$ or $|$Galactic latitude$|<10^\circ$ are excluded because these signals are mainly due to the Galaxy or bright sources. The dashed curve is the best-fitted Gaussian with $\mu =23.6\mu K$ and $\sigma =201.25\mu K$. $\chi^2 /DOF$ for the Gaussian fit is 4085.87/398 and the solid curve represents 2.6M-Gaussians fit with $\mu =23.6\mu K$, $\sigma_0 = 6682.22\mu K$ and $\sigma_{CMB}=80.25\mu K$. $\chi^2 /DOF$ for 2.6M-Gaussians fit is 435.76/398.
• Figure 3: Temperature distribution of full sky excluding the pixels with $|$Galactic latitude$| < 10^{\circ}$ or $|\Delta T| > 1mK$. Solid curve represents the best-fitted curve of uniformly distributed strings model and the dotted curve shows actual WMAP 1st-year data.
• Figure 4: $\chi^2$ distribution for the uniformly distributed strings model. $\chi^2_{min}=435.43$ with 398 degrees of freedom. Parameters span $0<\delta T<200.3\,\mu K$ and $192.1\,\mu K <\sigma<200.8\,\mu K$ at 95% CL. Here $\sigma^2$ represents the total variance except string contribution, $\sigma^2=\frac{\sigma^2_0}{N}\sum_{i}1/{n_i}+\sigma^{2}_{CMB}$. The outer contour is for 95% CL which is almost overlapped with the 68% CL contour in vertical direction.
• Figure 5: Generating the vector field $\vec{L}$. Pixels left demoted to middle pixels, middle $\rightarrow$ right: defining gradient of temperature $\nabla T$ and $\vec{L}$ which lies along temperature step.