Astroparticle Physics

280 13 Dark Mattertrue vacuumcosmological constantand static universecosmological constantas dominant energycould be liberated in a transition to the true vacuum (seeSect. 12.5).Paradoxically, a non-zero cosmological constant was introducedby Einstein as a parameter in the field equations ofthe theory of general relativity to describe a static universe,which was popular at that time and to prevent a dynamicbehaviour, which followed from his theory. Now it appearsthat the dominant energy, which determines the dynamics ofthe universe, is stored in the empty space itself. The questionnow arises, whether the cosmological constant is a practicablesupplement to the required dark matter. This questionwas controversial just as the question of the existence ofsupersymmetric particles or axions over the last years. Recently,however, several experiments have found compellingevidence for a substantial amount of dark energy, which canbe interpreted, e.g., in terms of a non-zero cosmological constant,see Chap. 12 on inflation.There is a fundamental difference between classical darkmatter in form of MACHOs, WIMPs, or axions and the effectof the cosmological constant Λ.The potential energy on a test mass m created by matterand the vacuum energy density can easily be written afterNewton to beE pot =−G mM matter− G mM vacuum energyRR∼− ϱ matterR 3− ϱ vacuumR 3. (13.23)R RThere is a fundamental difference between the matter den-sity and the vacuum energy density during the expansionof the universe. For the vacuum-energy term in (13.23) thevacuum energy density remains constant, since this energydensity is a property of the vacuum. In contrast to this thematter density does not remain constant during expansion,since only the mass is conserved leading to the dilution ofthe matter density. Therefore, the spatial dependence of thepotential energy is given bymatter densityvs. vacuum energy densityE pot ∼− M matterR− ϱ vacuum R 2 . (13.24)Since ϱ vacuum ∼ Λ, (13.24) shows that the radial dependenceof the mass term is fundamentally different fromthe term containing the cosmological constant. Therefore,the question of the existence of dark matter (M matter )anda