Astroparticle Physics

188 8 Cosmology24Ω m,0 ,Ω Λ,00.25,0.750.25, 01, 022SupernovaCosmologyProjecteffective m B201816Calan/Tololo& CfAFig. 8.6Magnitudes and residuals ofsupernovae of type Ia as a functionof redshift of their host galaxies incomparison to the expectation ofvarious models. The data areconsistent with a flat universe witha fraction of about 75% of darkenergy. Shown are data from theSupernova Cosmology Project, theCalan/Tololo group, and theHarvard–Smithsonian Center forAstrophysics (CfA) {26}mag. residualfrom empty cosmology141.00.50.00.51.00.0 0.2 0.4 0.6 0.8 1.0redshift zΩ m,0 ,Ω Λ,00.25,0.750.25, 01, 0accelerating universevacuum energyenergy, Ω m,0 = 1, i.e., Ω Λ,0 = 0, is in clear disagreement.The data are well described by Ω m,0 ≈ 0.25 andΩ Λ,0 ≈ 0.75. Further measurements of the cosmic microwavebackground support this view. This picture will becompleted in Chaps. 11 and 13.Qualitatively the behaviour shown in Fig. 8.6 can be understoodin the following way. The data points at high redshiftlie above the curve for zero vacuum energy, i.e., athigher magnitudes, which means that they are dimmer thanexpected. Thus the supernovae one sees at a given z are fartheraway than one would expect, therefore the expansionmust be speeding up.The exact physical origin of the vacuum energy remainsa mystery. On the one hand, vacuum energy is expected ina quantum field theory such as the Standard Model of elementaryparticles. Naïvely, one would expect its value to beof the orderϱ v ≈ E 4 max , (8.38)