References 207and the background energy densityρBat the time of beginning (this range can
span many tens of orders of magnitude, depending on the initial time), and will
anyway end on the tracker path before the present epoch, due to the presence of
an attractor in the phase space. In contrast, in the cosmological constant case, the
physical variableρis fixed once and for all at the beginning. This allows us to
state that in the quintessence case the fine-tuning issue, even if still far from being
solved, is at least weakened.
Much effort has recently been devoted to finding ways to constrain such
models with present and future cosmological data in order to distinguish
quintessence frommodels [60, 61]. An even more ambitious goal is the partial
reconstruction of the scalar field potential from measuring the variation of the
equation of state with increasing redshift [62].
Natural candidates for these scalar fields are pseudo-Goldstone bosons,
axions, e.g. scalar fields with a scalar potential decreasing to zero for an infinite
value of the fields. Such behaviour occurs naturally in models of dynamical
SUSY breaking: in SUSY models scalar potentials have many flat directions, that
is directions in the field’s space where the potential vanishes. After dynamical
SUSY breaking the degeneracy of the flat potential is lifted but it is restored for
infinite values of the scalar fields.
However, the investigation of quintessence models from the particle physics
point of view is just in a preliminary stage and a realistic model is not yet
available (see, for example, [63–66]). There are two classes of problems: the
construction of a field theory model with the required scalar potential and the
interaction of the quintessence field with SM fields [67]. The former problem
has already been considered by Bin ́etruy [63], who pointed out that scalar inverse
power law potentials appear in supersymmetric QCD theories (SQCD) [68] with
Nccolours andNf <Ncflavours. The latter seems the toughest. Indeed the
quintessence field today has typically a mass of orderQ 0 ∼ 10 −^33 eV. Then, in
general, it would mediate long range interactions of gravitational strength, which
are phenomenologically unacceptable.
References
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and Wiksells)
[2] Weinberg S 1967Phys.Rev.Lett. 191264
[3] Glashow S L 1961Nucl. Phys. 22579
[4] Peskin M E and Schroeder D V 1995An Introduction to Quantum Field Theory
(Reading, MA: Addison-Wesley)
[5] For an introduction to the DM problem, see, for instance: Kolb R and Turner S 1990
The Early Universe(New York: Addison-Wesley)
Srednicki M (ed) 1989Dark Matter(Amsterdam: North-Holland)
Primack J, Seckel D and Sadoulet B 1988Annu. Rev. Nucl. Part. Sci. 38751
[6] For a recent review see: Primack J 2000Preprintastro-ph/0007187