Measuring cosmological correlations


Cosmologists often attempt to measure small signals, from the 10-6 angular fluctuations in the brightness temperature of the comic microwave background (CMB), to the 10% enhancement in the correlation function of galaxies at 100 Mpc separations (resulting from baryons being dragged around by the CMB in the early Universe), to the weak 21cm emission signal from when the Universe was just several hundred million years young and still had most of its hydrogen in atomic form.  Since cosmological signals are nearly Gaussian random fields when smoothed over sufficiently large scales, one can write down the optimal method to measure them in this Gaussian limit.  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.


Recently Martin White and I investigated how to best infer the redshift distribution of galaxies with unknown redshifts by cross correlating them with galaxy populations for which the redshifts are ``known’’ via spectroscopy.  Since galaxies trace the same large-scale density field, the proximity of the unknown galaxies to the known galaxies allows  the inference of how well they trace each other in redshift.  It turns out that the optimal way to do this is simple and in certain very relevant limits boils down to intuitive analytic expressions.   The image below shows a 155 sq deg survey done by the Canada France Hawaii telescope.  Most of the objects are galaxies (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 such fields to learn their redshift distribution. 

In particular, we showed that it typically takes about 1000 sources with known redshifts per unit redshift to measure the redshift distribution of sources in the overlapping redshift interval (and does not depend on the angular density of known sources).  An important application of this technique is to calibrate redshift estimates of galaxies made from broad photometric bands.  Upcoming weak lensing surveys (aimed at precision cosmology) require extremely precise calibration of these redshifts in order for source redshift errors to not limit cosmological parameter determinations.


I have also worked on how much we can learn from 3D correlations in the Lyman-alpha forest. This measurement is one of the science drivers of the BOSS instrument on the Sloan telescope (part of SDSSIII) as well as future spectroscopic cosmological efforts such as msDESI.  The green region in the top panel shows a slice through a 3D map of the universe made with the BOSS instrument; the green shows the volume covered by 105 Lyman-alpha forest sightlines, which spans a volume larger than that covered by galaxies!

However, a few years ago it was unclear what sets the sensitivity to cosmological correlations in such a measurement (which must come from combination of S/N, quasar density, and spectral resolution) nor how a survey’s strategy should be optimized to maximize returns.  Martin White and I wrote a paper that attempted to answer these questions. Martin and I showed that the sensitivity of such surveys (given their volume) can be calculated to high accuracy from a single number, a S/N--weighted number density of quasars.  Our results allowed us and others to quickly investigate survey optimizations.  We showed that the BOSS quasar survey, which piggy-backs on the BOSS galaxies survey (the primary science goal of BOSS) and hence has little freedom in optimizing its strategy, is still close to the optimal quasar survey for this science on the Sloan telescope.