Search for cosmic strings in the Great Observatories Origins Deep Survey

We search Hubble Space Telescope Treasury Program images collected as part of the Great Observatories Origins Deep Survey for pairs of galaxies consistent with the gravitational lensing signature of a cosmic string. Our technique includes estimates of the efficiency for finding the lensed galaxy pair. In the north (south) survey field we find no evidence out to a redshift of greater than 0.5 (0.3) for cosmic strings to a mass per unit length limit of $G\mu /c^2<3.0\times {10}^{-7}$ at 95% confidence limits (C.L.). In the combined $314.9{\mathrm{arcmin}}^2$ of the north and south survey fields this corresponds to a global limit on ${\Omega }_{\mathrm{strings}}<0.02$. Our limit on $G\mu /c^2$ is more than an order of magnitude lower than searches for individual strings in cosmic microwave background (CMB) data. Our limit is higher than other CMB and gravitational wave searches, however, we note that it is less model dependent than these other searches.

Figure 1

Simulated cosmic strings at redshift 0.5 and 1.0 in a small part of the GOODS north field. Pairs of morphologically similar galaxies are expected to fall on opposite sides of the string.

Figure 2

Pairs of morphologically similar galaxies found in a region of the GOODS survey. These pairs form the background to the signal pairs from a cosmic string.

Figure 3

Correlations for random pairs of galaxies in the GOODS data (light gray points) compared to simulated signal (black points). We define matched galaxy pairs as those within the elliptical line at the top of the plot where the correlation and cross-correlation are optimal.

Figure 4

Pairs of galaxies in the GOODS north- and south-field data (points) compared to background (solid line) and one example of a simulated string (dashes). The upper simulated string is the total number of pairs expected from the simulation with string redshift of 1.2 and $\delta \sin \beta$ of $6^{\prime \prime }$. The lower simulated string includes measurement inefficiencies.

Figure 5

Various examples of simulated signals where $dN/d\Delta \theta$ represents the number of lensed galaxy pairs per angular separation distance as a function of cosmic string parameters—energy-density ($\delta \sin \beta$) and redshift ($z_l$). In these simulations, the number of signal events are scaled to a cosmic string with a total length of 10 arcminutes.

Figure 6

The ratio $D_{\mathrm{ls}}/D_{\mathrm{os}}$ is a multiplicative factor which affects the opening angle in Eq. (2). Here we plot it for a flat $\Lambda \mathrm{CDM}$ cosmology, $H_0=73\mathrm{km}/(\mathrm{s}\mathrm{Mpc})$, ${\Omega }_{\Lambda }=0.76$, ${\Omega }_M=0.24$.

Figure 7

Modeled GOODS north field source redshift probability distribution function (PDF) as a function of redshift and I-band magnitude (MAG_AUTO—shown on each curve). Distributions are scaled to the north field area ($A\simeq 160{\mathrm{arcmin}}^2$).

Figure 8

Efficiency of detecting pairs of galaxies lensed by a cosmic string as a function of pair opening angle. The correlation cut efficiencies are dependent on redshift as indicated. The other efficiencies are only weakly dependent on redshift.

Figure 9

Confidence limits at 95% for lensed galaxies produced by a cosmic string as a function of the string’s mass and redshift. The north field limits extend to higher redshifts due to statistical fluctuations of signal and background, and also because the mean string length across the survey is a bit longer and the number density of galaxies is somewhat higher.

Figure 10

Confidence limits at 95% on ${\Omega }_{\mathrm{string}}$ as a function of the string mass. The strongest limit occurs at the smallest string mass.