Astroparticle Physics

8.1 The Hubble Expansion 173isotropic and homogeneous when viewed over sufficientlylarge distances. It is in the context of this model that the lawsof particle physics will be applied in an attempt to trace theevolution of the universe at very early times. In this chapterthe important aspects of cosmology that one needs will bereviewed.Standard CosmologicalModel8.1 The Hubble Expansion“The history of astronomy is a historyof receding horizons.”Edwin Powell HubbleThe first important observation that leads to the StandardCosmological Model is Hubble’s discovery that all but thenearest galaxies are receding away from us (i.e., from theMilky Way) with a speed proportional to their distance. Thespeeds are determined from the Doppler shift of spectrallines. Suppose a galaxy receding from us (i.e., from theMilky Way) with a speed v = βc emits a photon of wavelengthλ em . When the photon is observed, its wavelengthwill be shifted to λ obs . To quantify this, the redshift z is definedasredshiftz = λ obs − λ em. (8.1)λ emFrom relativity one obtains the relation between the redshiftand the speed,√1 + βz =1 − β − 1 , (8.2)which can be approximated byz ≈ β (8.3)for β ≪ 1.To measure the distance of a galaxy one needs in ita light source of a calibrated brightness (a ‘standard candle’).The light flux from the source falls off inversely as thesquare of the distance r, so if the absolute luminosity L isknown and the source radiates isotropically, then the measuredlight flux is F = L/4πr 2 .Theluminosity distancecan therefore be determined from‘standard candle’luminosity distance