A direct probe of cosmological power spectra of the peculiar velocity
  field and the gravitational lensing magnification from photometric redshift
  surveys
  The cosmological peculiar velocity field (deviations from the pure Hubble
flow) of matter carries significant information on dark energy, dark matter and
the underlying theory of gravity on large scales. Peculiar motions of galaxies
introduce systematic deviations between the observed galaxy redshifts z and the
corresponding cosmological redshifts z_cos. A novel method for estimating the
angular power spectrum of the peculiar velocity field based on observations of
galaxy redshifts and apparent magnitudes m (or equivalently fluxes) is
presented. This method exploits the fact that a mean relation between z_cos and
m of galaxies can be derived from all galaxies in a redshift-magnitude survey.
Given a galaxy magnitude, it is shown that the z_cos(m) relation yields its
cosmological redshift with a 1-sigma error of sigma_z~0.3 for a survey like
Euclid (~10^9 galaxies at z<~2), and can be used to constrain the angular power
spectrum of z-z_cos(m) with a high signal-to-noise ratio. At large angular
separations corresponding to l<~15, we obtain significant constraints on the
power spectrum of the peculiar velocity field. At 15<~l<~60, magnitude shifts
in the z_cos(m) relation caused by gravitational lensing magnification
dominate, allowing us to probe the line-of-sight integral of the gravitational
potential. Effects related to the environmental dependence in the luminosity
function can easily be computed and their contamination removed from the
estimated power spectra. The amplitude of the combined velocity and lensing
power spectra at z~1 can be measured with <~5% accuracy.
