Cosmology without cosmic variance

We examine the improvements in constraints on the linear growth factor G and its derivative f = d lnG/d ln a that are available from the combination of a large-scale galaxy redshift survey with a weak gravitational lensing survey of background sources. In the linear perturbation theory limit, the bias-modulation method of McDonald & Seljak allows one to distinguish the real-space galaxy clustering from the peculiar velocity signal in each Fourier mode. The ratio of lensing signal to galaxy clustering in transverse modes yields the bias factor b of each galaxy subset, hence calibrating the conversion from galaxy real-space density to matter density in every mode. In combination these techniques permit measure of the growth rate f in each Fourier mode. In principle this yields a measure of the growth rate that is free of sample variance, i.e. the uncertainty in f can be reduced without bound by increasing the number of redshifts obtained within a finite survey volume. In practice, the gain from the absence of sample variance is bounded by the limited range of bias modulation among dark matter haloes. None the less, the addition of background weak lensing data to a redshift survey increases information on G and f by an amount equivalent to a 10-fold increase in the volume of a standard redshift-space distortion measurement - if the lensing signal can be measured to sub-per cent accuracy. This argues that a combined lensing and redshift survey over a common low-redshift volume of the Universe is a more powerful test of general relativity than an isolated redshift survey over larger volume at high redshift, especially as surveys begin to cover most of the available sky. An example case is that a survey of approximate to 10(6) halo redshifts over half the sky in the redshift range z = 0.5 +/- 0.05 can determine the growth exponent. for the model f = Omega(gamma)(m) to an accuracy of +/- 0.015, using only modes with k < 0.1 h Mpc(-1), but only if a weak lensing survey is conducted in concert.