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 settles. Peculiar motions of galaxies introduce systematic deviations between the observed galaxy redshifts z and the corresponding cosmological redshifts z(cos). A navel 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 at 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) similar to 0.3 for a survey like Euclid (similar to 10(9) galaxies at z less than or similar to 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 less than or similar to 15, we obtain significant constraints on the power spectrum of the peculiar velocity field. At 15 less than or similar to l less than or similar to 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 front the estimated power spectra. The amplitude of the combined velocity and lensing power spectra at z similar to 1 can be measured with less than or similar to 5% accuracy.