Can Topological Defects Mimic the BICEP2 $B$-Mode Signal?

We show that the $B$-mode polarization signal detected at low multipoles by BICEP2 cannot be entirely due to topological defects. This would be incompatible with the high-multipole $B$-mode polarization data and also with existing temperature anisotropy data. Adding cosmic strings to a model with tensors, we find that $B$ modes on their own provide a comparable limit on the defects to that already coming from Planck satellite temperature data. We note that strings at this limit give a modest improvement to the best fit of the $B$-mode data, at a somewhat lower tensor-to-scalar ratio of $r\simeq 0.15$.

Figure 1

The CMB temperature and polarization power spectra contributions from inflationary scalar modes (black solid lines), inflationary tensor modes (black dashed lines), and cosmic strings (blue dot-dashed lines) [16]. The inflationary tensors have $r=0.2$ whereas the string contribution has $f_{10}=0.03$.

Figure 2

$B$-mode polarization power spectra for textures (solid red line), semilocal strings (dashed black line), and Abelian Higgs strings (dot-dashed blue line). All the curves are normalized to make the temperature spectra match the Planck $\ell =10$ value. We see that all these types of topological defects predict similar shapes in the BICEP2 data range $30\lesssim \ell \lesssim 300$, though they become different for $\ell >300$.

Figure 3

Temperature (upper panel) and $B$-mode polarization (lower panel) power spectra compared to the Planck temperature and the BICEP2 $B$-mode polarization data. The black curve in the upper panel is the best-fit $\mathrm{\Lambda }\mathrm{CDM}$ model, and the blue dashed lines show the contribution from strings for $f_{10}=0.3$, 0.15, 0.06, and 0.03. The green-dotted curves in the lower panel show the combined contribution from strings and the lensing of the scalar perturbations, for the same values of $f_{10}$ as in the upper panel. The lowest dotted curve, for $f_{10}=0.03$, shows roughly the maximal allowed contribution from strings to the temperature power spectrum, given the Planck data. The highest dotted curve, $f_{10}=0.3$, matches the BICEP2 $B$-mode polarization at $\ell =80$. The gray dashed line is the sum of the $f_{10}=0.3$ string prediction with the Planck best-fit $\mathrm{\Lambda }\mathrm{CDM}$ model. The thin solid red line in the lower panel shows the combined contribution from the lensing of scalar perturbations and textures, normalized to match the $\ell =80$ BICEP2 data point.

Figure 4

A contribution from strings (blue dot-dashed lines) is added to the prediction from $r=0.15$ plus scalar lensing (solid black line) to give a total spectrum shown in gray lines. The data points are from BICEP2. From bottom to top, the string fractions are 0.015, 0.03, 0.04 (highlighted in red), and 0.06. A marginal improvement to the overall data fit is given for a string fraction around 0.04, which is about the maximum permitted by current constraints from Planck.