Dark matter and the deformed Poincar6 group

It has been recently suggested that models of deformed special relativity, based on a deformed Poincak group, could account for the missing mass problem, due to the nonadditivity of energy for large systems predicted by these models. We show that this is not correct and that, in fact, these models predict just the opposite effect. Recently, different explanations have been proposed to account for the missing mass problem. These explanations range from the existence of invisible brown dwarf stars (a “conservative” explanation) or the existence of a new kind of matter filling the universe (cold nonbaryonic dark matter), until more radical explanations proposing the need of new laws of physics [ 11. The missing mass problem arises when astronomers look at the rotation curves of galaxies (i.e. the pattern of the velocities of stars around a galaxy). They find that, in order to get the galaxies clumped, it would be necessary to have much more mass inside them than observed. The “observed” mass refers to the estimated mass of galaxies obtained counting the “visible” mass (stars, HII regions, molecular gas clouds, etc.). Thus, we have an “observed” mass and a “dynamical” mass (the latter is obtained assuming the approximate validity of Newton’s gravitational laws). The same happens with galaxies inside clusters of galaxies. The dynamical mass is of the order of 10-100 times the observed mass. Thus, a lot of research has been devoted in order to account for the missing mass. In par’ E-mail: [email protected]. titular, models of “deformed” special relativity, based on a deformed Poincart5 Group [ 2-61 show that energy is not additive for large systems in these models, this means that the total energy of the universe would not be proportional to the number of particles it contains. This implies that for large systems, the mass “observed” will differ from the real mass. We will not enter the details of the theory of deformations of the Poincarb group. In Ref. [ 71 all physically acceptable deformed Poincart5 algebras are classified and the advantages of such deformations are resumed. Recently, MaSlanka [ 81 proposed a parametrization of a family of deformed Poincark groups which has been used by Bacry 161 to study the nonadditivity of energy and to suggest that this could account for the missing mass (so that there would be no dark matter to discover). We will show that this family of deformed Poincart5 groups is not useful in explaining a mass defect. In fact, it predicts the opposite observed effect, posing doubts about its validity as a model of the real physical world. If we denote by J, K, P and PO the generators of the ordinary Poincart group (which generate rotations, 0370-2693/96/%12.00