Retrieving the three-dimensional matter power spectrum and galaxy biasing parameters from lensing tomography

Abstract

Aims. 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. Methods. 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 two-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. Results. For a relatively deep 200 deg2 survey (0.9) with 30 sources per square arcmin, the matter power spectrum can be probed with 3-6σ significance on comoving scales 1 ≈ k h-1 Mpc ≈ 10 and z ≈ 0.3. For 3 lenses per square arcmin, a significant detection (∼10σ) of the galaxy-matter power spectrum and galaxy power spectrum is attainable to relatively high redshifts (z ≈ 0.8) and over a wider k-range. Within the Bayesian framework, all three power spectra are easily combined to provide constraints on 3D galaxy biasing parameters. Therein, weak priors on the galaxy bias improve constraints on the matter power spectrum. Conclusions. A shear tomography analysis of weak-lensing surveys in the near future promises fruitful insights into both the effect of baryons on the nonlinear matter power spectrum at z ≈ 0.3 and galaxy biasing (z ≈ 0.5). However, a proper treatment of the anticipated systematics, which are not included in the mock analysis but discussed here, is likely to reduce the signal-to-noise ratio in the analysis such that a robust assessment of the 3D matter power spectrum probably requires a survey area of at least ∼10 3 deg2. To investigate the matter power spectrum at redshift higher than ∼0.3, an increase in survey area is mandatory. © 2012 ESO.