We present the first measurement of weak lensing by large-scale structure on scales of 1 - 4 degrees based on radio observations .
We utilize the FIRST Radio Survey , a quarter-sky , 20 cm survey produced with the NRAO Very Large Array ( VLA ) .
The large angular scales afforded by the FIRST survey provide a measurement in the linear regime of the matter power spectrum , thus avoiding the necessity of applying uncertain non-linear corrections .
Moreover , since the VLA interferometer has a well-known and deterministic beam , our measurement does not suffer from the irreproducible effects of atmospheric seeing which limit ground-based optical surveys .
We use the shapelet method described in an earlier paper to estimate the shear from the shape of radio sources derived directly from the interferometric measurements in the Fourier ( uv ) plane .
With realistic simulations we verify that the method yields unbiased shear estimators .
We study and quantify the systematic effects which can produce spurious shears , analytically and with simulations , and carefully correct for them .
We measure the shear correlation functions on angular scales of 0.5 ^ { \circ } -40 ^ { \circ } , and compute the corresponding aperture mass statistics .
On 1 ^ { \circ } -4 ^ { \circ } scales , we find that the B-modes are consistent with zero , and detect a lensing E-mode signal significant at the 3.0 \sigma level .
After removing nearby radio sources with an optical counterpart , the E -mode signal increases by 10-20 % , as expected for a lensing signal derived from more distant sources .
We use the E-mode measurement on these scales to constrain the mass power spectrum normalization \sigma _ { 8 } and the median redshift z _ { m } of the unidentified radio sources .
We find \sigma _ { 8 } ( z _ { m } / 2 ) ^ { 0.6 } \simeq 1.0 \pm 0.2 where the 1 \sigma error bars include statistical errors , cosmic variance , and systematics .
This is consistent with earlier determinations of \sigma _ { 8 } from cosmic shear , the cosmic microwave background ( CMB ) and cluster abundance , and with our current knowledge of the redshift distribution of radio sources .
Taking the prior \sigma _ { 8 } = 0.9 \pm 0.1 ( 68 % CL ) from the WMAP experiment , this corresponds to z _ { m } = 2.2 \pm 0.9 ( 68 % CL ) for radio sources without optical counterparts , consistent with existing models for the radio source luminosity function .
Our results offer promising prospects for precision measurements of cosmic shear with future radio interferometers such as LOFAR and the SKA .