My research interests center on large scale structure and cosmology, specifically the intersection of data, measurement and theory. As current and future surveys like the SDSS, LSST and PanSTARS increase our knowledge base, exploiting the full potential of these resources will require the ability to integrate these three areas in a cohesive manner. Only then will we be able to address the fundamental physics behind processes like the formation of galaxies and the behavior of dark energy.

Over the past two years, we have also used this data set along with maps from the Wilkinson Microwave Anisotropy Probe (WMAP) to measure the induced cross-correlation between the foreground large scale structure and background cosmic microwave background radiation. The large-angle component of this cross-correlation comes as a result of the ISW effect -- the late decay of gravitational potentials due to accelerated cosmological expansion. For a flat universe, this serves as a direct probe of the existence of dark energy. Taking advantage of the galaxy color information available with the SDSS, we were able to select a sub-population of galaxies (luminous red galaxies) from the SDSS data and further subdivide them into four deep redshift slices. By statistically combining the cross-correlations of these slices with the CMB maps from WMAP (a single cross-correlation is shown in Figure 1), we found a statistically significant detection of the induced cross-correlation, a clear signature of dark energy.

During the last year, we have combined the photometric galaxy and quasar catalogs to measure the cosmic magnification of the background quasars by foreground large scale structure. Weak gravitational lensing by the foreground matter induces a small correlation between the two distinct populations, making the background quasars brighter but diluting their surface density on the sky. A number of previous attempts have been made at this measurement but they routinely disagreed with both the predicted signal and each other. With our superior control over sources of systematic errors in both the galaxy and quasar data sets as well as a much higher density of quasars on the sky, we were able to detect the expected lensing signal at the 8 sigma level. Thanks to the broad dynamic range of the photometric data, we were also able to measure the expected angular variation of the signal on physical scales ranging from 60 kpc/h to 10 Mpc/h (Figure 2). Demonstrating that the expected magnification signal can be reliably detected opens up a parallel track for all future weak lensing surveys, complementing shear measurements and providing a crucial check on systematic biases.

To make measurements over such a wide, densely filled area feasible, we have developed SDSSPix: a hierarchical, equal-area pixelization of the sphere built around the SDSS geometry. By integrating this method into our angular correlation function algorithms, I have been able to reduce the typical running time by upwards of three orders of magnitude. Measurements on our current data set actually take far less processing time than our previous results, despite a factor of 40 increase in area. Without such an improvement, determining the statistical errors for our current measurements (to say nothing of measuring higher order moments) would be effectively impossible.

Multi-band imaging surveys give us the power to divide galaxies on the basis of color, morphology, luminosity, and the like. With a few modest extensions to the standard formalism, halo model theories can make predictions for these sub-populations while maintaining the character of the total population. In this extension, we ultimately want to describe the population of dark matter halos by galaxies -- the halo occupation density (HOD) -- not just as a function of halo mass, but also galaxy type, luminosity and so on. My thesis applied this new formalism to the expected angular clustering in the final SDSS data set, finding that, in the simple case considering a volume-limited sample split into red and blue sub-populations, one could expect to constrain the parameters describing the HOD to better than 10%.

In addition to galaxy clustering, one can also extract information about the HOD using magnification bias -- an induced cross-correlation between background and foreground objects due to weak lensing. This effect is a function of the number of galaxies in a halo on small scales, while the auto-correlation is a function of the number of galaxy pairs within a halo on those scales. As such, the combination should give us an excellent description of the first two moments of the HOD, given the expected errors from the completed SDSS photometric survey.

On the dark energy front, current and future meaurements of the ISW will likely provide relatively weak constraints on standard cosmological parameters. However, as we show in our paper, combining the ISW, galaxy auto-correlation, and weak lensing results from a full-sky deep galaxy survey may be singularly useful in other ways. In particular, measuring the scale for dark energy clustering (if one exists) is extremely difficult with most cosmological statistics. Despite the relatively poor statistical significance of the ISW signal for an optimal survey (S/N ~ 10), the nature of the effect is such that one could constrain the clustering of dark energy to 3% precision at Gpc scales.