CMB power spectrum contribution from cosmic strings using field-evolution simulations of the Abelian Higgs model

TL;DR

This work delivers the first field-theory calculation of the CMB temperature power spectrum contribution from cosmic strings by simulating the Abelian Higgs model on a lattice, exploiting scaling to extend the dynamic range, and using unequal-time correlators of the energy-momentum tensor to drive CMB perturbations. The authors implement a UETC-based framework with an eigenvector decomposition to convert field data into coherent sources for a modified CMBEASY calculation, enabling full-sky spectra across relevant scales. They find a string normalization of $G\mu$ near $2\times10^{-6}$ when normalized to the WMAP data at $\ell=10$, and show that local strings produce a broader peak dominated by vector modes compared to prior Nambu-Goto or texture-based approaches. The results illuminate the role of decay products and non-linear string dynamics in shaping the CMB spectrum and point toward future polarization constraints and high-precision data from Planck for tighter limits on cosmic strings.

Abstract

We present the first field-theoretic calculations of the contribution made by cosmic strings to the temperature power spectrum of the cosmic microwave background (CMB). Unlike previous work, in which strings were modeled as idealized one-dimensional objects, we evolve the simplest example of an underlying field theory containing local U(1) strings, the Abelian Higgs model. Limitations imposed by finite computational volumes are overcome using the scaling property of string networks and a further extrapolation related to the lessening of the string width in comoving coordinates. The strings and their decay products, which are automatically included in the field theory approach, source metric perturbations via their energy-momentum tensor, the unequal-time correlation functions of which are used as input into the CMB calculation phase. These calculations involve the use of a modified version of CMBEASY, with results provided over the full range of relevant scales. We find that the string tension $μ$ required to normalize to the WMAP 3-year data at multipole $\ell = 10$ is $Gμ= [2.04\pm0.06\textrm{(stat.)}\pm0.12\textrm{(sys.)}] \times 10^{-6}$, where we have quoted statistical and systematic errors separately, and $G$ is Newton's constant. This is a factor 2-3 higher than values in current circulation.

Figures (14)

• Figure 1: Slices through a $512^{3}$ simulation in the radiation era, showing the Abelian Higgs analogue of magnetic flux density. Magnetic flux tubes run along the cosmic strings, which appear as dark regions, with a shape dependent upon the nature of the string intersection with the slice. Varying left to right, the horizon size (measured as $2\tau$) is 0.35, 0.63 and 1.00 times the box-side while the string width decays inversely with the scale factor $a$ and hence as $\tau^{-1}$ ($a \propto \tau$). Note the decay products visible in these images.
• Figure 2: The variation of the string width $r$ and coupling parameters with conformal time $\tau$ (in units of $\phi_{0}^{-1}$) for the $s\!=\!0.3$ simulations described in Section \ref{['sec:IniCon']}. The subscript 0 indicates the value at the end of the simulation.
• Figure 3: Results for the Lagrangian measure of $\xi$ from 5 simulations in the radiation era with $s\!=\!1$ (top) and $s\!=\!0$ (lower). The shaded regions show the $1\!-\!\sigma$ and $2\!-\!\sigma$ variations in the mean (error bars have not been used since correlations extend across most of the plot and would tempt the reader into believing individual points were independent). The best-fit straight lines over the region $80\phi_{0}^{-1}<\tau<128\phi_{0}^{-1}$ ($s\!=\!1$) and $64\phi_{0}^{-1}<\tau <128\phi_{0}^{-1}$ ($s\!=\!0$) are also shown. Note that for the later case, this excludes the acausal final period.
• Figure 4: The raw equal-time scaling function $\tilde{C}^{\mathrm{S}}_{11}(k\tau,k\tau)$ as averaged over 5 realizations for $s\!=\!0.3$ in the radiation era. Results are plotted at roughly uniformly-spaced $\tau$ values in the range $64\phi_{0}^{-1}<\tau<128\phi_{0}^{-1}$. The lower lines correspond to increasingly early times (dashed), with the $1\!-\!\sigma$ and $2\!-\!\sigma$ uncertainties in the mean indicated for the latest time (solid).
• Figure 5: The equal-time scaling function $\tilde{C}^{\mathrm{S}}_{11}(k\tau,k\tau)$ as in the previous figure, but with the time offset taken into account. For present plot, the mean offset across the 5 realizations is used to adjust results for each one, whereas the actual CMB calculations use independent offsets for each realization.