Observational Evidence for Weak Gravitational Lensing by Large Scale Structure

A single very deep $10'$ field has been imaged to $r \sim 26$. There are 2682 galaxies with $23 \le r \le 26$ with a size significantly larger than the seeing disk in the field. After correcting for telescope aberrations, possible guiding errors, and signal degradation due to seeing, I find a polarization signal of amplitude $|p|=2.7\%$, with an uncertainty of 1.2\% (95\% confidence limit). For the 1773 galaxies with $23 \le r \le 25$, the measured amplitude is 2.4\% $\pm$ 1.2\% (95\% confidence limit). If this observed polarization is due to gravitational lensing by large scale structure, cosmological inferences can be made. The polarization amplitude would indicate that $\Omega_0 \times \sigma_8 \approx 1$. The amplitude probability distribution is a Rayleigh distribution with variance $\sigma_p^2$ so the probability $P(1/2 < |p|/\sigma_p <2) = 75\%$, and $P(1/3 < |p|/\sigma_p < 3) = 93.5\%$. The measurement of the polarization amplitude in a single field can be used to constrain cosmological models since $\sigma_p \propto \Omega_0 \times \sigma_8$.