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BA-TH/00-397\\
gr-qc/0009098
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{\Large\bf\centering\ignorespaces
Production and Detection of Relic Dilatons \\
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in String Cosmology
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M. Gasperini
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Dipartimento di Fisica, Universit\`a di Bari,\\
Via G. Amendola 173, 70126 Bari, Italy \\
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and\\
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Istituto Nazionale di Fisica Nucleare, Sezione di Bari, Bari, Italy\\
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\centerline{\bf Abstract}
\noindent
This paper summarizes the contribution presented at the {\sl IX Marcel
Grossmann Meeting} (Rome, July 2000). It is stressed, in particular, that
a non-relativistic background of ultra-light dilatons, produced in the
context of string cosmology, could represent today a significant
fraction of cold dark matter. If the dilaton mass lies within the
resonant band of present gravitational antennas, a stochastic dilaton
background with a nearly critical density could be visible, in
principle, already at the level of sensitivity of the detectors
in operation and presently under construction.
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Contributed paper to the {\bf IX Marcel
Grossmann Meeting} (Rome, July 2000)\\
To appear in the Proceedings (World Scientific, Singapore)
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\title{Production and Detection of Relic Dilatons \\ in String Cosmology}
\author{M. Gasperini}
\address{Dipartimento di Fisica, Universit\`a di Bari, and INFN, Sezione
di Bari, \\Via G. Amendola 173, 70126 Bari, Italy
\\E-mail: gasperini@ba.infn.it}
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\abstracts{\centerline{Preprint No. BA-TH/00-397; ~~~~~~~E-print
Archives: gr-qc/0009098}}
%\section{Guidelines}
%\subsection{Producing the Hard Copy}\label{subsec:prod}
The main purpose of this paper is to point out that the relic dilatons
produced in the context of the pre-big bang scenario \cite{1} could
provide a significant contribution to the present fraction of dark
matter density and, if light enough, could be detectable even by
present gravitational antennas \cite{2}, provided their coupling to
macroscopic bodies is not too far from the present experimental upper
limits.
The spectrum of the relic dilatons, produced from the vacuum
through the parametric amplification of quantum fluctuations, differs
from the graviton spectrum because of the mass of the dilaton, and
contains in general three branches \cite{3}, corresponding to
\begin{itemize}
\item{}
relativistic modes, with proper momentum $p=k/a > m$;
\item{}
non-relativistic modes, with $p_m < p0$, to
avoid infrared divergences. It follows that the relativistic branch of
the spectrum is growing, and it is bounded today by the peak value
$\Omega_\chi^{\rm rel} \sim (H_1/M_p)^2 \Omega_\gamma \laq
10^{-6}$, where we have used the fact that the final inflation scale is
controlled by the string mass scale $H_1 \simeq M_s \sim (0.1 - 0.01)
M_p$.
The non-relativistic part of the spectrum, on the contrary, is only
constrained by the critical density bound,
\begin {equation}
\int^m d \ln p
\Omega_\chi^{\rm non-rel}(p) \laq 1.
\end{equation}
Let us suppose that $\delta <1$,
so that the above integral is dominated by the peak of the spectrum at
$p=p_m$, and leads to the constraint
\begin {equation}
\Omega_\chi (p_m) \simeq \left(H_1\over M_p \right)^2
\left(m\over H_{\rm eq}\right)^{1/2} \left(m\over H_1\right)^{\delta/2}
\laq 1.
\end{equation}
If this constraint is
saturated, i.e. if the dilaton mass satisfies
\begin{equation}
m \simeq (H_{\rm eq} M_p^4 H_1^{\delta-4})^{1/(\delta+1)},
\label{2}
\end{equation}
then the non-relativistic branch dominates the dilaton spectrum, and
the relic dilatons might represent a significant fraction of the present
cold dark matter density. It is important to stress that, for a nearly flat
spectrum ($\delta \rightarrow 0$), this may occurr even for very low
masses, lying in the sensitivity range of gravitational antennas. If we
take, for instance, $m \sim 1$ kHz $\sim 10^{-12}$ eV, and $H_1=M_s
\sim 10^{-1}M_p$, then the condition (\ref{2}) is satified for $\delta
\simeq 11/39 \simeq 0.28$.
It is not impossible, therefore, that the very weak (much
smaller than gravitational) coupling to the detectors of ultra-light
dilatons \cite{4} may be compensated by a very high (almost critical)
relic energy density (much higher than for relic gravitons). If this is the
case, an analysis of the signal-to-noise ratio produced by a
non-relativistic stochastic background of scalar particles \cite{2}
shows that the detection of a dilatonic dark matter component is in
principle compatible with the expected sensitivity of the gravitational
antennas in operation and presently under construction.
\begin{thebibliography}{99}
\bibitem{1}M. Gasperini and G. Veneziano,
\Journal{\PRD}{50}{2519}{1994}; \\M. Gasperini,
\Journal{\PLB}{327}{314}{1994}.
\bibitem{2}M. Gasperini,
\Journal{\PLB}{477}{242}{2000};
\Journal{\PLB}{470}{67}{1999}.
\bibitem{3}M. Gasperini and G. Veneziano,
\Journal{\PRD}{59}{43503}{1999}.
\bibitem{4}T. Damour and A. M. Polyakov,
\Journal{\NPB}{423}{532}{1994}.
\end{thebibliography}
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