| Summary: | The advent of wide-field galaxy surveys with high quality imaging provides an opportunity to map the dark matter distribution in large parts of the visible Universe. However, the available probes of the large-scale structure have distinct properties. In particular, galaxies are a high resolution but biased tracer of mass, while weak lensing avoids such biases but, due to low signal-to-noise ratio, has poor resolution. After reviewing the applications of maps in cosmology, I investigate the relation between the Fourier phases of cosmological fields. By considering Gaussian random fields, I take some steps in describing the statistics of phase difference. Then I consider some simple models of realistic cosmological fields galaxies and weak gravitational lensing. I find that a linear bias evolving in redshift leads to a scale independent phase difference, whereas shot noise and stochasticity lead to a scale dependent phase difference. I investigate reconstructing the projected density field using the complementarity of weak lensing and galaxy positions. I propose a maximum probability reconstruction of the 2D lensing convergence with a likelihood term for shear data and a prior on the Fourier phases constructed from the galaxy positions. By considering only the phases of the galaxy field, the method evades the unknown value of the bias and allows it to be calibrated by lensing on a mode-by-mode basis.
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