Astroparticle Physics

13.3 Problems 285map of about 1 ◦ indicates – according to theory – that theuniverse is flat. If the results of the supernova project (seeSect. 8.3), the WMAP results, and the Boomerang and Maximadata are combined, a value for the cosmological constantcorresponding to Ω Λ ≈ 0.7 is favoured. Such a significantcontribution would mean that the vacuum is filledwith an incredibly weakly interaction substance, which revealsitself only via its repulsive gravitation (e.g., in termsof a quintessence model). The suggested large contributionof the vacuum energy to the Ω parameter would naturallyraise the question, whether appreciable amounts of exoticdark matter (e.g., in the form of WIMPs) are required at all.However, it appears that for the understanding of the dynamicsof galaxies and the interpretation of the fluctuations inthe blackbody temperature a contribution of classical, nonbaryonicdark matter corresponding to Ω dm ≈ 0.23 is indispensable.In this scenario the long-term fate of the universe is characterizedby eternal accelerated expansion. A Big Crunchevent as anticipated for Ω larger than unity appears to becompletely ruled out. Since the nature of the dark energyis essentially unknown, also its long-term properties are notunderstood. Therefore, one must be prepared for surprises.For example, it is possible that the dark energy becomes sopowerful that the known forces are insufficient to preservethe universe. Galactic clusters, galaxies, planetary systems,and eventually atoms would be torn apart. In such theoriesone speculates about an apocalyptic Big Rip, which wouldshred the whole physical structure of the universe at the endof time.flat universevacuum energyBig CrunchBig Rip13.3 Problems1. In the vicinity of the galactic center of the Milky Waycelestial objects have been identified in the infrared andradio band which appear to rotate around an invisiblecenter with high orbital velocities. One of these objectscircles the galactic center with an orbital velocity of v ≈110 km/s at a distance of approximately 2.5 pc. Workout the mass of the galactic center assuming Kepleriankinematics for a circular orbit!2. What is the maximum energy that a WIMP (m W = 100GeV) of 1 GeV kinetic energy can transfer to an electronat rest?