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\subsection{The dark matter distribution in the Universe on large
scales as seen with weak gravitational lensing} %Please give
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{\bf{
{Prof. Peter Schneider}\\
{Institut f. Astrophysik u. Extraterrestrische Forschung}\\
{Universit\"at Bonn}\\
{Auf dem H\"ugel 71}\\
{D-53121 BONN}\\
{Telefon: 0228/733671}\\
{Fax: 0228/734022}\\
{Email: peter@astro.uni-bonn.de}\\}}


\subsubsection{Abstract}
The nature and spatial distribution of dark matter in the Universe is
the central issue of modern cosmology. Weak gravitational
lensing, the distortion of distant faint galaxy images by the tidal
gravitational effect of intervening matter, provides an ideal tool to
study the dark matter distribution, as the light deflection depends on
the total (dark + luminous) mass distribution. The statistical
properties of the distortion field, that can be obtained from the
image ellipticities, immediately translates to the statistical
properties of the dark matter distribution, the large-scale structure
(LSS). Aim of this project is to exploit this novel technique to
constrain the properties of the LSS.


\subsubsection{Current status of research}
Weak gravitational lensing (see Mellier 1999; Bartelmann \& Schneider
2001 for recent reviews) employs the fact that light bundles are
distorted when propagating through an inhomogeneous matter
distribution; the corresponding tidal fields change the observable
image ellipticity of distant sources in a predictable way. Since the
extragalactic sky is densely filled with faint galaxies, the
statistical investigation of their image shapes directly yields
information about the (statistical properties of the) matter
distribution in the Universe. For example, any two-point statistics of
the corresponding distortion field -- also called shear -- yields a
weighted average over the power spectrum of the LSS, which by itself
is one of the central quantities to describe the Universe and
structure formation. Although this connection had been known for quite
some time (e.g., Blandford et al. 1991; Kaiser 1992), only in 2000 was
this effect discovered, by four independent teams (Bacon et al. 2000;
Kaiser et al. 2000; van Waerbeke et al. 2000a; Wittman et
al. 2000). Progress became possible through the great advances in
optical detector arrays and in image analysis procedures. A further
detection of cosmic shear has been reported very recently (van
Waerbeke et al. 2000b), based on observations carried out with the new
Very Large Telescope. In this paper, the measured results on cosmic
shear were used to derive a relation between the normalization of the
power spetrum $\sigma_8$ and the density parameter $\Omega_0$ of the
Universe. It turned out that the derived relation is in very good
agreement with the normalization based on the local abundance of
massive galaxy clusters. Since the latter depends not only on the
power spectrum, but also on the statistical nature of the density
field -- usually assumed to be gaussian -- this close agreement is a
very strong hint for the Gaussianity of the primordial density
fluctuations.

Beside the two-point statistics, the cosmic shear data carry
substantially more information about the properties of the LSS. As has
been pointed out by Bernardeau et al. (1997), Schneider et al. (1998),
van Waerbeke et al. (1999), Kruse \& Schneider (1999, 2000), Jain et
al. (2000), and others, higher-order statistics, such as the skewness
or the peak probability distribution, can be used to test the standard
gravitational instability theory for structure growth, the redshift
dependence of the power spectrum, and therefore the cosmological
parameters $\Omega_0$ and $\Lambda$. 


\subsubsection{Own experience}
The proposer has been leading a group on gravitational lensing
research for about 10 years in which more than 100 refereed
publications were written. He first-authored the monograph on the
topic (Schneider, Ehlers \& Falco 1992). The group played a
leading role in the development of weak gravitational lensing, both in
theory (see Bartelmann \& Schneider 2001 and references therein) and
from an observational point-of-view (e.g., Seitz et al. 1997; Erben et
al. 2000; Clowe et al. 2000). Our group has also deeply been involved
in the development of cosmic shear analysis (Schneider et al. 1998;
Schneider 1998; van Waerbeke 1998, Kruse \& Schneider 1999, 2000;
Reblinsky et al. 1999), and participated in the first detections of
the cosmic shear signal (van Waerbeke et al 2000a,b). Furthermore, our
group leads a major observational effort to observe cosmic shear with
the Hubble Space Telescope, for which 1200 parallel orbits have been
assigned. 

\subsubsection{Goals of the project}
The goal of this project is to exploit cosmic shear in order to
obtain the strongest constraints on the LSS and therefore to provide
invaluable input to cosmology. Taking into account the near-term
perspectives in observational astronomy (e.g., the newly-built
wide-field imaging telescopes VST and VISTA, the MEGACAM project at
the CFHT etc.) we shall have in the near future a greatly increased
amount of data usable for this goal. Therefore the following steps
shall be taken:
\begin{itemize}
\item
Continued participation in the observational programs and the data
analysis. This part of the project will be carried out in very close
collaboration with the group in Paris, led by Y. Mellier (IAP), and
partly with a group at the ST/ECF at ESO, led by W. Freudling.
Members of our group (D. Clowe, T. Erben, M. Schirmer) have 
extensive experience in these aspects. Preparation for, and analysis
of the VST photometric data will be the focus of this aspect.
\item
Theoretical predictions and statistical analysis. Given that the
density field in the Universe is highly non-Gaussian at later times,
there is no unique prescription for the optimal extraction of
cosmological information from the cosmic shear data. Several
statistical measures have been suggested, each of them providing one
particular 
view of the picture. The data material will soon become sufficiently
large that such optimal extraction methods need to be developed. The
fact that we have been able to obtain a first cosmological constraint
from cosmic shear measurements (van Waerbeke et al. 2000b) shows that
this new cosmological tool has matured. The future possibilities to
take photometric redshift information into account when analyzing
cosmic shear data need to be explored; a preliminary analysis (Hu
1999) shows that the power-spectrum estimate can be improved by a
significant amount when this redshift information is accounted for. 
\item
Refinement of cosmic shear extraction from observations. Whereas
detailed investigations have shown that shear signals of the order of
1\% can certainly be extracted from deep images of a quality now
routinely achieved at the best astronomical sites, it is still unclear
whether shears below 1\% can be detected, i.e., separated from
systematics coming from PSF anisotropies, distorting telescope optics
etc. Such small values of the shear are expected on angular scales
above $\sim 20'$ which probe the linear regime of structure formation
at late times. These scales are of particular importance as they
permit a direct comparison with CMB data; together, these two methods
will be able to {\it directly prove} the gravitational instability
picture of structure growth and significantly increase the precision
of cosmological parameter estimates from CMB measurements alone (Hu \&
Tegmark 1999).
\end{itemize}

\subsubsection{Estimate of resources expected from DFG}
The long time-span between the realization of the potential of cosmic
shear and its first detection indicates the complexity of the
technical aspects of this research area. In order to make proper use
of the upcoming wide-field imaging data, an experienced researcher is
needed who is able to carry out the data analysis using
state-of-the-art methods. This can only be done by an experienced
post-doctoral researcher who shall also take part of the
responsibilities of maintaining the computer system for this project.
Given the current sophistication of power-spectrum extraction from
noisy data, as has been pioneered for the purpose of the analysis of
future CMB data, a significant improvement in the quantitative
analysis of cosmic shear data requires the involvement of a post-doc
with considerable experience in statistical methods -- preferably
someone who has been involved with one of the CMB teams. The
investigation of the limitations of cosmic shear measurements via
simulations and analytical estimates provides an ideal dissertation
project which shall be supervised jointly by the proposer and the
post-doctoral researcher working on the wide-field imaging data.

\subsubsection{Members of research group relevant for the project}
Prof. Peter Schneider, Dr. Douglas Clowe, Dr. Marco Lombardi,
Dipl. Phys. Thomas Erben, Dipl. Phys. Hannelore H\"ammerle,
Dipl. Phys. Michael Schirmer

\subsubsection{Connections to other projects of current SFB proposal}
Schau mer mal

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