  After defining conformal Galilean-type algebras for arbitrary dynamical
exponent $z$ we consider the particular cases of the conformal Galilei algebra
(CGA) and the Schr\"odinger Lie algebra (sch). Galilei massless particles
moving with arbitrary, finite velocity are introduced \begin{description}
\item{i)} in $d=2$ as a realization of the centrally extended CGA in 6
dimensional phase space, \item{ii)} in arbitrary spatial dimension $d$ as a
realization of the unextended \it{sch} in 4d dimensional phase space.
\end{description} A particle system, minimally coupled to gravity, shows,
besides Galilei symmetry, also invariance with respect to arbitrary time
dependent translations and to dilations with $z = (d +2)/3$. The most important
physical property of such a self-gravitating system is the appearance of a
dynamically generated gravitational mass density of either sign. Therefore,
this property may serve as a model for the dark sector of the universe. The
cosmological solutions of the corresponding hydrodynamical equations show a
deceleration phase for the early universe and an acceleration phase for the
late universe. This paper is based, in large part, on a recent work with W.J.
Zakrzewski: Can cosmic acceleration be caused by exotic massless particles?
arXiv:0904.1375 (astro-ph.CO) [1].
