Using galaxy-galaxy weak lensing measurements to correct the finger of God

For decades, cosmologists have been using galaxies to trace the large-scale distribution of matter. At present, the largest source of systematic uncertainty in this analysis is the challenge of modelling the complex relationship between galaxy redshift and the distribution of dark matter. If all galaxies sat in the centres of haloes, there would be minimal finger-of-God (FoG) effects and a simple relationship between the galaxy and matter distributions. However, many galaxies, even some of the luminous red galaxies (LRGs), do not lie in the centres of haloes. Because the galaxy-galaxy lensing is also sensitive to the off-centred galaxies, we show that we can use the lensing measurements to determine the amplitude of this effect and to determine the expected amplitude of FoG effects. We develop an approach for using the lensing data to model how the FoG suppresses the power spectrum amplitudes and show that the current data imply a 30 per cent suppression at wavenumberk= 0.2h Mpc ^-1. Our analysis implies that it is important to complement a spectroscopic survey with an imaging survey with sufficient depth and wide field coverage. Joint imaging and spectroscopic surveys allow a robust, unbiased use of the power spectrum amplitude information: it improves the marginalized error of growth ratef _g≡ d ln D/d ln aby up to a factor of 2 over a wide range of redshiftsz< 1.4. We also find that the dark energy equation-of-state parameter,w ₀, and the neutrino mass,f _ν, can be unbiasedly constrained by combining the lensing information, with an improvement of 10-25 per cent compared to a spectroscopic survey without lensing calibration.