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\subsection{Supersymmetry and the early universe} %Please give
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{\bf{
{Prof. Dr. Hans Peter Nilles}\\
{Physikalisches Institut}\\
{Universit\"at Bonn}\\
{Nussalles 12}\\
{D-53115 BONN}\\
{Telefon: 0228/73-3247}\\
{Fax: 0228/73-3223}\\
{Email: nilles@th.physik.uni-bonn.de}\\}}


\subsubsection{Abstract}

We investigate the supersymmetric extension of the
$SU(3)\times SU(2)\times U(1)$ standard model of strong,
weak and electromagnetic interactions. This generalization 
predicts various new particles (like
neutralinos, axinos, gravitinos among others)
that might be relevant
for cosmological and astrophysical applications. 
One aspect of the research concentrates on the possibility
that these particles
could be realistic candidates for cold dark 
matter observed 
in the universe. We would like to explore the 
various theoretical schemes and their implications for the
properties of dark matter, also in view of the experimental
efforts to detect these particles directly. 
A second aspect concerns the question of new symmetries
and their relevance for rare processes as e.g. proton decay
and related cosmological consequences like the creation
of a baryon asymmetry in the early universe.


\subsubsection{Current status of research}

The $SU(3)\times SU(2)\times U(1)$ standard model of particle
physics describes practically all known microphysical phenomena.
Its predictions have been successfully tested within the last two
decades. Nonetheless there are various theoretical questions
that could not been answered in this framework and that led
to the study of extensions, the most popular of which is the one
based on supersymmetry. This theory has attracted much attention in
the last ten years not only in the field of particle physics but also 
in view of its possible relevance for cosmology and astrophysics.
A central prediction is the existence of a stable, neutral, massive
and weakly interacting particle, now believed to be a neutralino:
a supersymmetric partner of one of the neutral gauge bosons that mediate
the weak and electromagnetic interactions. Mass and interactions of
this particle could be in a range that leads to a relevant 
cosmological abundance and make this particle a candidate for
cold dark matter in the universe. By now various classes of
models are well understood and the cosmic relic abundance can be
computed. What is less well understood are theoretical arguments
in favour of one or the other model. It is believed that the mechanism
of spontaneous supersymmetry breakdown is relevant for the
specific properties of these models, but more work is needed to
draw a final conclusion.

The investigation of properties of could dark matter has concentrated
mainly on the size of the relic abundance. More detailed questions
concerning the spatial distribution of dark matter still have to 
be answered.

One of the arguments for a generalization of the standard model of
electroweak interactions is the fact that it does not lead to
a satisfactory explanation of the baryon asymmetry of the early
universe. Here as well the supersymmetric generalization of the
models offers various alternatives that have to be explored
in detail.

\subsubsection{Own experience}

Members of this group have been among the pioneers of the
supersymmetric extension of the standard model \cite{Nilles} 
and have
experience in the particle physics as well as cosmological
appication of this scheme. Specifically we have an expertise
in the study of the mechanism of supersymmetry breakdown
and the determination of the resulting soft breaking parameters.
Theoretical concepts like the embedding of the models in
string theory have been studied recently \cite{NOY1}. This 
resulted in a specific pattern of masses for neutralinos that
have consequences for their relic abundance \cite{Kawamura}.
We are currently trying to examine this question in connection
with a possible existnce of a nonvanishing value of the
cosmological constant along the lines of earlier 
work \cite{CKN}.


\begin{thebibliography}{99}


\bibitem{Nilles} H.\ P.\ Nilles {\it ``Supersymmetry, Supergravity and
    Particle Physics''}, {\it
    Phys.\ Reports\ } {\bf C110} (1984) 1.

\bibitem{NOY1} H.\ P.\ Nilles, M.\ Olechowski and M.\ Yamaguchi, {\it
    ``Supersymmetry breaking and soft terms in M theory''}, {\it
    Phys.\ Lett.\ } {\bf B415} (1997) 24, {\tt hep-th/9707143}.

\bibitem{Kawamura} 
    Y.\ Kawamura, H.\ P.\ Nilles, M.\ Olechowski and M.\ Yamaguchi,
    {\it ``Relic abundance of neutralinos in heterotic string theory:
    weak coupling vs. strong coupling''}, {\it JHEP} {\bf 9806},
    (1998), 008, {\tt hep-ph/9805397};

\bibitem{CKN} K.\ Choi, J.\ E.\ Kim and H.\ P.\ Nilles, {\it
    ``Cosmological constant and soft terms in supergravity''}, {\it
    Phys.\ Rev.\ Lett.} {\bf 73} (1994) 1758, {\tt hep-ph/9404311}

\end{thebibliography}
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\subsubsection{Goals of the project}

We would like to clarify detailed properties of dark matter
candidates that appear in the supersymmetric extension of the
standard model. This does not just concern the value of the
relic abundance and the fact that these relics are cold, but
also more specific questions of e.g. self interactions that might
be relevant for the distribution of dark matter in the universe.
One such question aims at the abundance of dark matter at the 
center of our galaxy and its possible influence on the central
black hole. 

Moreover, present experimental searches, like the ones at
accelerators as LEP and the Tevatron restrict the possible
candidates for dark matter. Direct searches for WIMPs in our
galaxy (e.g. DAMA) seem to give positive evidence at a quite
unexpected range, but this result is not confirmed and even
questioned (CDMS experiment).

The nature and the properties of dark matter candidates depend
crucially on the mechanism of supersyemmtry breakdown and this is 
one of the central research efforts in our group. It is here that
more formal questions having to do with supergravity,
unification of coupling constants, string theory and extra
dimensions come into play. Current data on (lower) limits on the
mass of the supersymmetric partners (not just the dark matter
candidate LSP) contrain these models more and more, and give therefore
useful indirect information on the LSP.

The models are matured in the meantime in such a way that one can 
begin to simulate the distribution of dark matter candidates in
collaboration with astronomers that have prepared the
calculational tools. 

Meanwhile we have learned, that the contribution of dark matter
$\Omega_M$ to the critical density is not 1 but more between
0.3 and 0.5 while $\Omega_M + \Omega_\Lambda$ is of order unity,
with $\Omega_\Lambda$ a contribution that might correspond to
a constant vacuum energy (a cosmological constant). Central
questions, why this gives critical density and what is the size
of the individual contributions have to be addressed from the
theoretical point a view. Up to now we have treated these numbers as 
parameters that have to be determined by experimental
observations and it seems now the time to look at this from the
viewpoint of the underlying theory and its consistency. In fact,
we have to see how the relic abundance of the dark matter in its 
dependence on the soft supersymmetry breaking parameters might
be influenced by the presence of a cosmological constant or
the vacuum energy of a slowly varying field (quintessence), which in 
turn might be connected to the mechanism of inflation in the 
early universe.

Supersymmetry leads to models of unification of strong, weak and
electromagnetic interactions in so-called grand unified theories
(GUTs) at a high scale, where bryon number is violated, a
mechanism necessary for the generation of a net baryon asymmetry
in the universe. The interrelation of this mechanism with the
rate of proton decay in GUT theories has to be studied also in view
of upcoming experiments that probe the predictions of the 
simplest model.


\subsubsection{Estimate of resources expected from DFG}

\begin{itemize}

\item 1 postdoc position 

\item 1 PhD student?

\item travel money 

\item money for invitations

\end{itemize}


\subsubsection{Members of research group relevant for the project}

\begin{itemize}

\item Prof. H. P. Nilles

\item Dr. D. Ghilencea

\item R. Schreyer

\item M. Hillenbach

\end{itemize}

International collaborations with Ibanez(Madrid), Masiero(Triete),
Antonadis(Paris), Ross(Oxford) and Barbieri(Pisa).

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

Connections to High enery experiments, Brock, Hilger, Kobel, Wermes:
related theory Dreiner, Nahm and astronomers, Biermann, Falcke,
Schneider.



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