Astroparticle Physics

8.2 The Isotropic and Homogeneous Universe 175For the distances covered in the plot, the data are clearlyin good agreement with a linear relation,v = H 0 r, (8.5)which is Hubble’s Law. The parameter H 0 is Hubble’s constant,which from the data in Fig. 8.1 is determined to be64 (km/s)/Mpc. Here the subscript 0 is used to indicate thevalue of the parameter today. The relation between speedand distance is not, however, constant in time.Determinations of the Hubble constant based on differentobservations have yielded inconsistent results, althoughless so now than a decade ago. A compilation of data from2004 concludes a value ofHubble’s constantH 0 = 71 ± 5 (km/s)/Mpc , (8.6)with further systematic uncertainties of 5 to 10% [2]. In addition,one usually defines the parameter h byh parameterH 0 = h × 100 (km/s)/Mpc . (8.7)Quantities that depend on H 0 are then written with the correspondingdependence on h. To obtain a numerical value onesubstitutes for h the most accurate estimate available at thetime (h = 0.71 +0.04−0.03in 2004). For purposes of this courseone can use h ≈ 0.7 ± 0.1.8.2 The Isotropic and Homogeneous Universe“The center of the universe is everywhere,and the circumference isnowhere.”Giordano BrunoThe assumption of an isotropic and homogeneous universe,sometimes called the cosmological principle, was initiallymade by Einstein and others because it simplified the mathematicsof general relativity. Today there is ample observationalevidence in favour of this hypothesis. The cosmic microwavebackground radiation, for example, is found to beisotropic to a level of around one part in 10 5 .The isotropy and homogeneity appear today to hold atsufficiently large distances, say, greater than around 100megaparsecs. At smaller distances, galaxies are found tocosmological principleisotropy and homogeneity