Astroparticle Physics

11.6 Determination of Cosmological Parameters 241where z ≈ 1100 is the redshift of the surface of last scattering.Thus, if a region is considered whose size was equal tothe particle-horizon distance at the time of last scattering asgiven by (11.17) as viewed from today, then it will subtendan angleθ ≈ 3t ls − t 2/3lstmr1/3(1 + z) (11.20)3t 0950 000 a180◦≈3 × 1.4 × 10 10 × 1100 ×a π ≈ 1.4◦ .The structure at or just below this angular scale correspondsto the ‘acoustic peaks’ visible in the power spectrum startingat around l ≈ 200.The naming of the structures in the power spectrumas ‘acoustic peaks’ comes about for the following reason:as already mentioned, the density fluctuations in the earlyuniverse caused gravitational instabilities. When the matterfell into these gravitational potential wells, this matterwas compressed, thereby getting heated up. This hot matterradiated photons causing the plasma of baryons to expand,thereby cooling down and producing less radiation as a consequence.With decreasing radiation pressure the irregularitiesreach a point where gravity again took over initiatinganother compression phase. The competition between gravitationalaccretion and radiation pressure caused longitudinalacoustic oscillations in the baryon fluid. After decouplingof matter from radiation the pattern of acoustic oscillationsbecame frozen into the CMB. CMB anisotropies thereforeare a consequence of sound waves in the primordial protonfluid.The angle subtended by the horizon distance at the timeof last scattering depends, however, on the geometry of theuniverse, and this is determined by Ω, the ratio of the energydensity to the critical density. This is illustrated schematicallyin Fig. 11.5. In Fig. 11.5(a), Ω = 1isassumedandtherefore the universe is described by a flat geometry. Theangles of the triangle sum to 180 ◦ and the angle subtendedby the acoustic horizon has a value a bit less than 1 ◦ . If,however, one has Ω