Retrieving the three-dimensional matter power spectrum and galaxy
  biasing parameters from lensing tomography
  With the availability of galaxy distance indicators in weak lensing surveys,
lensing tomography can be harnessed to constrain the three-dimensional (3D)
matter power spectrum over a range of redshift and physical scale. By combining
galaxy-galaxy lensing and galaxy clustering, this can be extended to probe the
3D galaxy-matter and galaxy-galaxy power spectrum or, alternatively, galaxy
biasing parameters. To achieve this aim, this paper introduces and discusses
minimum variance estimators and a more general Bayesian approach to
statistically invert a set of noisy tomography 2-point correlation functions,
measured within a confined opening angle. Both methods are constructed such
that they probe deviations of the power spectrum from a fiducial power
spectrum, thereby enabling both a direct comparison of theory and data, and in
principle the identification of the physical scale and redshift of deviations.
By devising a new Monte Carlo technique, we quantify the measurement noise in
the correlators for a fiducial survey, and test the performance of the
inversion techniques. We conclude that a shear tomography analysis of near
future weak lensing surveys promises fruitful insights into the effect of
baryons on the nonlinear matter power spectrum at z<~0.3 around k~2 h/Mpc, and
into galaxy biasing (z<~0.5). However, a proper treatment of anticipated
systematics -- not included in the mock analysis but discussed here -- is
likely to reduce the signal-to-noise in the analysis so that a robust
assessment of the 3D matter power spectrum probably asks for a survey area of
at least 1000 sdeg. [Abridged]
