Fitting Cosmic Microwave Background Data with Cosmic Strings and Inflation

We perform a multiparameter likelihood analysis to compare measurements of the cosmic microwave background (CMB) power spectra with predictions from models involving cosmic strings. Adding strings to the standard case of a primordial spectrum with power-law tilt $n_s$, we find a $2\sigma$ detection of strings: $f_{10}=0.11\pm 0.05$, where $f_{10}$ is the fractional contribution made by strings in the temperature power spectrum (at $\ell =10$). CMB data give moderate preference to the model $n_s=1$ with cosmic strings over the standard zero-strings model with variable tilt. When additional non-CMB data are incorporated, the two models become on a par. With variable $n_s$ and these extra data, we find that $f_{10}<0.11$, which corresponds to $G_{\mu }<0.7\times {10}^{-6}$ (where $\mu$ is the string tension and $G$ is the gravitational constant).

Figure 1

The temperature power spectrum contribution from cosmic strings, normalized to match the WMAP data at $\ell =10$, as well as the best-fit cases from inflation only (model PL) and inflation plus strings ($\mathrm{PL}+\mathrm{S}$). These are compared to the WMAP and BOOMERANG data. The lower plot is a repeat but with the best-fit inflation case subtracted, highlighting the deviations between the predictions and the data. Note that the string contribution is identical to that shown in Fig. 14 of 5, but here has a linear horizontal axis for $\ell >100$.

Figure 2

The 2D marginalized likelihood distributions from CMB data (only) for $f_{10}$ versus $h$, ${\Omega }_b{h}^2$, $A_s^2$, and $n_s$. Contours show the 68% and 95% confidence regions for model $\mathrm{PL}+\mathrm{S}$ while the 400 MCMC points indicate the preferred region for $\mathrm{HZ}+\mathrm{S}$. The vertical lines on the $h$ and ${\Omega }_b{h}^2$ plots show the 68% and 95% confidence limits from the HKP and BBN measurements.