The Dynamics of Clusters of Galaxies in Universes with Non-Zero Cosmological Constant, and the 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 M VT/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.