Constraints on the Fundamental String Coupling from $B$-Mode Experiments

We study signatures of cosmic superstring networks containing strings of multiple tensions and $Y$ junctions, on the cosmic microwave background (CMB) temperature and polarization spectra. Focusing on the crucial role of the string coupling constant $g_s$, we show that the number density and energy density of the scaling network are dominated by different types of string in the $g_s\sim 1$ and $g_s\ll 1$ limits. This can lead to an observable shift in the position of the $B$-mode peak—a distinct signal leading to a direct constraint on $g_s$. We forecast the joint bounds on $g_s$ and the fundamental string tension ${\mu }_F$ from upcoming and future CMB polarization experiments, as well as the signal to noise in detecting the difference between $B$-mode signals in the limiting cases of large and small $g_s$. We show that such a detectable shift is within reach of planned experiments.

Figure 1

Dependence of the rms velocity (top), correlation length (middle), and power spectrum density (bottom panel) at the time of last scattering (LS) on the value of the string coupling $g_s$ for the $F$ strings (solid black lines), $D$ strings (blue dashed lines) and $FD$ strings (red dotted lines). The rms velocity and correlation length of the string type(s) dominating the power spectrum are shown with oversized dots.

Figure 2

The $B$-mode power spectra for $g_s=0.04$ (solid lines) and $g_s=0.9$ (dashed lines) normalized to $f_s=0.1$. The insert plot shows the position of the peak as a function of $g_s$.

Figure 3

The dot-dashed (black) curves show an $f_s$ of (from top-to-bottom) 0.1, 0.01, 0.001 and 0.0001 in the (${\mu }_F$, $g_s$) parameter plane. Other curves show the $S/N=5$ contours of an overall detection of the $B$-mode signal for various experiments. The three curves for each experiment show the pessimistic (long-dashed lines), realistic (short-dashed lines) and optimistic (solid lines) scenarios for the removal of lensing $B$ modes, as discussed in the text. We also show the pulsar bounds based on data in 20 (dot-dot-dot-dashed lines) in the small (upper curve) and large (lower curve) string loop limits considered in 11, 18.

Figure 4

The $S/N$ of an overall detection (lower panel) as a function of $f_s$ for a reference model with $g_s=0.1$. Labels are the same as in Fig. 3, with the sets of three curves (showing the optimistic, realistic and pessimistic lensing scenarios) from left to right. The upper panel shows the $S/N$ of the difference signal between two models with $g_s=0.04$ and $g_s=0.9$, with these both having the same overall detection $S/N$ of the reference model at fixed $f_s$.