DATA ANALYSIS TOOLS FOR COSMOLOGY

Ben Granett *graduate student*

Peter Papai *graduate student*

Jun Pan

Gang Chen

**Detecting Dark Energy with Supervoids and Superclusters:**

We have a strong measurement of dark energy using supervoids and superclusters
identified in the Sloan Digital Sky Survey. Find out more.

**The Sound of the Universe: **

We turned the measurements of the Cosmic Microwave
Background by WMAP
into sound. We believe that totally new aspects of the data are opened up
when it is turned into a soundscape.
Hear it for yourself!

We tried to be as faithful to the original data as possible while still obtaining fairly musical results. We used the Tegmark Wiener filtered map in Healpix format with N_side=512 resolution. We turned all of the approximately 3 million pixels into a sound file where the sound represents a "cosmic path" through the sky, spiraling down from the north pole through the equator to the south pole. The higher pitch in the beginning and the end are artifacts of the pixelization and the route taken. Note that this is a mono recording.

An alternative representation of the CMB as sound using only the power spectrum has been previously done by Mark Whittle. Our method differs in that it preserves what is called the "full phase information". In other words it represents in detail our particular Universe as opposed to an ensemble of universes in an average sense. The musical quality thus comes from a combination of aggressive noise reduction of the original map and from the full information kept.

**Statistical Analysis of Large Astronomical Data Sets: **

We are developing a suite of new methods and
algorithms for spatial statistical
analyses of future large astronomical data bases, such as
galaxy catalogs (SDSS), megapixel CMB maps
(e.g., WMAP and
Planck).
Contemporary data analysis tools
are inadequate for future large data sets, even with the most powerful
supercomputers existing or projected. The new approach consists of a
powerful mixture of advanced computer science, statistics, and group theory.
As an example, standard analysis of megapixel
CMB maps from Planck would take a million years on hypothetical computers
equipped with TeraBytes of memory. The new analysis suite
created by Szapudi and collaborators, SpICE (Spatially Inhomogeneous
Correlation Estimator) brings an order of billion fold improvement,
enabling the analysis of WMAP and Planck in less then 5 and 40 minutes,
respectively. In addition to megapixel CMB maps,
the novel methods developed in this research will
be immensely useful for joint analysis of
future surveys across several wavelengths, as
envisioned in the planned National Virtual Observatory (NVO) framework.
In addition Euclidean version (eSpICE) as well as generalization
for polarization of the CMB and higher order statistics has been
developed.
We have recently fully reanalyzed WMAP first year data, which presently is
the only independent analysis outside the WMAP team.
Further details and data
products can be found here.

**Galaxy Clustering, Bias, and Dark Energy:**

Another of our major lines of research is the study of higher order statistics
in galaxy catalogs, such as the Sloan Digital Sky Survey (SDSS).
Statistical properties of large scale structure are represented
primarily through the distribution of galaxies, but
the underlying dark matter, which appears to dominate the
matter content of the universe, might have an entirely different
distribution. This phenomenon commonly known as galaxy ``bias'' plays a central
role in modern cosmology. Its understanding potentially
constrains the nature and distribution of Dark Matter,
one of the most interesting issues of 21st century physics.
Yet, at present, it constitutes the weakest link in our theories of
structure formation. Higher order statistics
sheds new light on these phenomena (Szapudi & Pan 2003),
and new measurements will translate into tight constraints on the nature and
distribution of the dark matter, on Gaussianity of the initial conditions,
and on the physics of galaxy formation. Recent results included
the first detection of the Dark Energy via cross-correlating
SDSS galaxies with CMB measurements by WMAP (Fosalba et al. 2003, Scranton et al. 2003).

**Dark Matter Dynamics via Wave Mechanics:**

We have been working on a wave mechanical
description of the growth of fluctuations in dark matter fields.
This approach has unique advantages compared to previous techniques:
it is formally simpler and allows to describe shell crossing (where Euler's
equations fail) as its free of the caustics/infinities which
plague the BBKGY and Boltzmann formulation (Szapudi & Kaiser 2003). In addition,
a wave simulation technique can be formulated, which is {\em fundamentally
different} from N-body simulations, hence has different systematics.
Perturbation theory of the WKB approximation
of the wave mechanical equations have been persued. The
results are extremely encouraging: the log of the density field emerged
as natural variable from which one can recover almost exactly
next-to-leading orders (loop corrections) in Perturbation Theory
what is an almost intractable problem in the standard Eulerian formalism.

**Correlation functions/Power spectrum:**
SpICE[Info, Download], eSpICE[Download]

**Counts-in-cells: **
pnsw2-3, pnf2-3, BMW-PN

**Theoretical Cosmology Suite: **
CosmoPy [Info] [Preview Download]

NASA ATP NAG5-12101 (2002-2005): "Novel Techniques for Fast CMB Analysis"

NSF AST02-06243 (2002-2005): "Constraining Bias via Clustering in Galaxy Surveys"

NSF ITR 1120201-128440 (2002-2006): "Statistical Data Mining for Cosmology"

NSF AMS04-0434413 (2004-2007): "Information Repackaging via Multi-resolution Transforms"