DYNAMICS OF CLUSTERS OF GALAXIES IN UNIVERSES WITH NON-ZERO COSMOLOGICAL CONSTANT, AND VIRIAL THEOREM MASS DISCREPANCY

The effects on groups of galaxies of a non-zero cosmological constant are considered. A version of the virial theorem which includes a cosmological term is derived. It is shown that a negative value of λ, in the region - 10-34 s-2 to - 10-33 s-2, can account quite well for the well-known virial theorem mass discrepancy in actual clusters. The theorem predicts that a graph of log MVT/M against log (cluster mean density) should be a straight line with slope - 0.5; the observed value is - 0.43 ± 0.08. It is proved that this effect could be responsible for the discrepancy only in universes with curvature index k = - 1. The Universe ages corresponding to the above range of A values are calculated; they are shorter than currently accepted values, but, it is argued, not impossibly so. © Royal Astronomical Society.