Conformal Galilean-type algebras, massless particles and gravitation

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].