On vector mode contribution to CMB temperature and polarization from local strings

TL;DR

The paper addresses significant coding errors in the cosmic-string contribution to CMB anisotropy, notably a missing vector-mode normalization and a general spectrum normalization factor. By correcting these, vector-mode power increases dramatically (approximately by a factor of $8$) and all string spectra are renormalized, leading to a tighter bound on the string tension: $G\mu_0 \approx 1.1 \times 10^{-6}$ and $G\mu < 1.8\,(2.7) \times 10^{-7}$ (68/95% c.l.). The improved vector contribution also greatly enhances the predicted B-mode polarization from cosmic strings, by roughly $10$–$20$ times, making a string-sourced BB signal potentially observable and possibly exceeding lensing-induced B modes. These results motivate reanalysis with newer CMB data (e.g., WMAP3) and have implications for constraining or detecting cosmic strings via B-mode polarization.

Abstract

In a recent publication, we used the data from WMAP and SDSS to constrain the primordial perturbations and to predict the B-mode polarization sourced by cosmic string networks. We have been alerted by A. Slosar to the existence of errors in the code we used to calculate the Cosmic Microwave Background anisotropies from cosmic strings. Correcting the errors leads to a significant increase in the vector mode contribution to the CMB temperature and polarization anisotropies as well as an overall renormalization of the various string spectra. In these notes we explain the nature of the errors and discuss their implications for previously published constraints on cosmic strings based on this code. The chief change in our results is that our derived limit for the cosmic string tension is strengthened: Gμ< 1.8 (2.7) * 10^{-7} at 68 (95)% confidence. We also note that the newly-enhanced vector mode contribution produces a greatly-increased amplitude for B-mode polarization in the CMB which could exceed the B-mode power produced by the lensing of primordial E-mode polarization into B-mode polarization.

Figures (2)

• Figure 1: The scalar (blue dot), vector (red short dash), tensor (black long dash) and their sum (solid black) contributions to the CMB TT spectrum evaluated using the old (left) and the revised (right) codes for the cases of smooth ($\alpha_r=1$) and wiggly ($\alpha_r=1.9$) strings with $G\mu = 1.4 \times 10^{-6}$. The spectra are proportional to $(G\mu)^2$ and this value of $G\mu$ corresponds to the reference cosmic string tension used in our previous work WPW05, divided by $\sqrt{2}$ (to correct an overall factor of two missing in the power spectra computed from the previous version of our code). Comparing the old and revised plots, it is evident that the new smooth string spectra have a factor of about $1.69$ higher amplitude than the old spectra for the same string tension. We combine these two corrections -- a factor of $\sqrt{2}$ in overall normalization and a factor of $\approx \sqrt{1.69}$ from enhanced vector modes -- to infer that the correct, fiducial cosmic string tension should be $G\mu_0 \approx 1.1 \times 10^{-6}$, which is a factor of $1.8$ smaller than the fiducial tension estimated in our previous work. The meaning of this fiducial tension, explained in our last paper, is this: $G\mu_0$ is the cosmic string tension that would be necessary for a network of cosmic strings to produce the same integrated primordial power as is found in the WMAP best-fit adiabatic model. The parameter $\alpha_r$ is the ratio of the effective mass-per-length of a wiggly string to that of a smooth string in the radiation era. See Refs. PV99WPW05 for further details on string substructure.
• Figure 2: The CMB BB spectra. Left: the plot from our last paper WPW05 showing contributions from inflation for $r=0.1$ (dash-dot), lensing (dot) and cosmic strings (solid line for smooth and dash line for wiggly). Right: revised predictions for the smooth (solid, red) and wiggly (dashed, blue) cases based on the assumption that strings contribute $10$% of the power in the CMB TT spectrum. Inflation and lensing estimates are plotted as in the left hand panel but with the inflationary tensor mode color-coded magenta and E to B lensing still black.