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\subsection{Inflation and  nonthermal production of
gravitini} %Please give
                                                        %title here

{\bf{
{Prof. Dr. Hans Peter Nilles and Dr. Marco Peloso}\\
{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}

The mechanism of inflation in the early universe solves some
cosmological puzzles as the horizon and flatness problems. 
Simple toy models exhibit the basic properties of inflation,
but many detailed questions remain unanswered. One of these
questions is the production of particles at the end of inflation.
In the framework of broken supersymmetry, the gravitino could
be overproduced thermally as well as nonthermally. While the
former is not a major obstacle to realistic model building the
latter has been argued to be a severe problem. We try to
answer this question through direct calculations in a variety of
models. We hope that these restrictions will narrow down the
number of models for a succesfull inflationary mechanism,
and lead to more refined predictions that have to be worked out
and confronted with observations.

\subsubsection{Current status of research}

There exist many schemes of inflation, like old, new, chaotic, extended
inflation (just to name a few) that try to provide a particle physics
description of this mechanism. Usually a given model concentrates on
a specific question, but a full satisfactory scheme has not yet been found.
Especially the mechanism of supersymmetry breakdown is usually 
ignored within this discussion. If one tries to calculate the
abundance of various field after the inflationary epoch, one is often
faced with severe problems. One of them is the possible overproduction
of the gravitino. This question has been addressed in the literature
up to now only in one-field models with unbroken supersymmetry
\cite{Linde,Giudice}. It is not clear to us (nor to anybody else)
what these observations really imply.


\subsubsection{Own experience}

We came across this problem at the COSMO99 meeting in Trieste
in discussions with Kallosh, Kofman and Linde, who claimed that
there is a severe problem with the nonthermal overproduction 
of gravitini at the end of inflation. We pointed out to them that
their conclusion was premature and that a more complete model
was needed to address this question. Meanwhile M. Peloso 
\cite{Peloso} has
worked out a code to compute the nonthermal production of   
particles in inflationary models with several scalar fields and
broken supersymmetry. Specifically we also want to analyze models
based on D-term inflation
discussed in earlier work of ours \cite{Lavignac}


\begin{thebibliography}{99}


\bibitem{Linde} R. Kallosh, L. Kofman, A. Linde and A. van Proeyen,
    {\it ``Gravitino production after inflation''}, {\it
    Phys.\ Rev.\ } {\bf D61} (2000) 103503, {\tt hep-ph/9907124}.

\bibitem{Giudice} G. Giudice, I. Tkachev and A. Riotto, {\it
    ``Nonthermal production of dangerous relics in the early
      universe''}, {\it
      JHEP} {\bf 9908} (1999) 009, {\tt hep-ph/9907510}.

\bibitem{Peloso} 
    M. Peloso and L. Sorbo,
    {\it ``Preheating of massive fermions after inflation:
     analytical results''}, {\it JHEP} {\bf 0005},
    (2000), 016, {\tt hep-ph/0003045}.

\bibitem{Lavignac} Z.\ Lalak, S. Lavignac and H.\ P.\ Nilles, {\it
    ``String dualities in the presence of U(1) symmetries''}, {\it
    Nucl.\ Phys.} {\bf B559} (1999) 1758, {\tt hep-ph/9903160}.

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

We would like to clarify the question of gravitino production
(as well as production of string moduli) in the process of 
preheating and reheating
after inflation. At the moment this appears to be a serious problem,
since all existing models point at an  overproduction of these
relics. However, in many of these models the question of
supersymmetry breakdown has not been addressed in a satisfactory way.
We will set up various representative classes of models with
exhibit inflation in the presence of supersymmetry breakdown.
One of them incorporates the Polonyi superpotential, while others
are derived from more abstract supergravity models making use
of Fayet-Iliopoulos terms. We then intend to compute the
production of inflatinos and gravitinos numerically using methods
developed by Peloso and coworkers. 

These calculations will shed light on some basic questions
concerning the coupling (decoupling) of the goldstone fermion
in local (global) supersymmetry in the early universe. 
During the period of inflation, supersymmetry is broken even 
if the groundstate of the theory at zero temperature is 
supersymmetric. Thus the nature of the candidate goldstino is
time dependent and the ``real'' goldstino (that is the longitudinal
component of the gravitino at zero temperature) might not
be produced during reheating. One attempt to avoid an overproduction
of gravitini could therefore be a decoupling of the ``real'' goldstino
from the inflaton multiplet at the level of global supersymmetry.
The coupling would then be purely gravitational, possibly avoiding
a dangerous relic density.

String moduli, i.e. light scalar fields that parametrize
the vacuum degeneracy of superstring theories might suffer from
the same problem as gravitini. Here as well, one has to discuus
possible solutions to this problem.

Given these calculations, it has to be expected that a solution
of the problem of overproduction of dangerous relics will only
be possible within a very restrictive class of models of
inflation, and therefore pose severe restrictions on the
mechanism of inflation itself. In fact, a successful mechanism 
of inflation will necessarily be linked with a satisfactory
mechanism of supersymmetry breakdown. With the results expected
from the considerations above, we would then be led to
a quite restrictive set of multi-field models with a chance
to realistically describe exponential expansion in the early 
universe. 

This restricted set of models would then have to be investigated in
detail with respect to generic predictions of the mechanism of
inflation, that would be linked to phenomena in particle physics
through the mechanism of supersymmetry breakdown. This would then
allow us to see whether some of the theoretically favoured models,
like chaotic inflation or D-term inflation are surviving the test
of consistency from other cosmological considerations like
the relic density of gravitini and string moduli.



\subsubsection{Estimate of resources expected from DFG}

\begin{itemize}

\item 1 postdoc position 

\item 1 PhD student?

\item travel money 

\item money for invitation

\end{itemize}


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

\begin{itemize}

\item Prof. H, P. Nilles 

\item Dr. M. Peloso

\item Dr. S. Groot Nibbelink

\item J. Conrad

\item G. Honecker

\end{itemize}


International collaborations with Quiros(Madrid), Masiero(Triete),
Binetruy(Paris), Sarkar(Oxford) and Giudice(CERN).

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

Connections to work that deals with cosmic background radiation.... 



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