Cosmological Measurement Theory

I often worry about how well one can measure small cosmological signals, from the baryon acoustic oscillation scale, to different radio lines, to anisotropies in the CMB.  Since the cosmological signal is nearly Gaussian on > few Mpc scales, one can write down the optimal method to measure large scale cosmological signals.  Sometimes the optimal method is not practical to apply to real data or does not reduce to intuitive expressions, but sometimes this exercise is quite fruitful.

The latter holds for a project I recently finished with Martin White. There we investigated how to best to infer the redshift distribution of galaxies from cross correlating them with populations for which the redshifts are known from spectroscopy.  Since galaxies trace the same large-scale density field, the proximity of the unknown galaxies to the know galaxies allows one to infer their closeness.  It turns out that the optimal way to do this is quite simple and in certain very relevant limits boils down to simple analytic expressions.   The picture below shows a 155 sq deg survey done by the Canada France Hawaii telescope.  Most of the objects in it are galaxies (and there are 38  million objects that have been identified in the high resolution version of this image).  This is just one of many deep galaxy surveys we have of the sky.  Our method can be applied to different types of extragalactic sources in this field to learn their redshift distribution. 

So, if you want to estimate how well you can measure the redshift distribution of sources from cross correlating with known sources, our paper gives simple formulae for how successful you will likely be and for how to do this optimally.  We show that it typically takes about 1000 known sources per unit redshift to measure the distribution of sources in that redshift interval (and does not depend on the density of known sources).

In a separate study, Martin and I also looked at the how well 3D correlations in the Lyman-alpha forest can be constrained.  This measurement is one of the science drivers of the BOSS instrument, but it was unclear what sets the noise level in such a measurement and how survey strategy should be optimized to maximize returns.   For such surveys, the noise turns out to come from the aliasing high-k modes that results from the weird window function of these surveys.  Martin and I showed that the noise formula nevertheless reduce to a simple form.  These results can be used to quickly investigate survey optimizations.