Heller M, Woodin W.H. (eds.) Infinity. New research frontiers (CUP, 2011)(ISBN 1107003873)(O)(327s)_MAml_

198 infinity and the nostalgia of the starsl(l+1)C l /2π[μK 2 ]Angular scale90° 2° 0.5°600050004000300020000.2°WMAPAcbarBoomerangCBIVSA1000010100500Multipole moment l10001500Figure 9.1. Measurements of the angular power spectrum of the CMB radiation. The oscillatingpattern results from acoustic oscillations in the primordial plasma. The best fit yields accuratemeasurements of cosmological density parameters. The angular scale of the main peak, about1 degree, is directly related to the total energy density, and its value indicates that cosmicspace is very nearly Euclidean. The thickness of the model line represents the cosmic variancelimit. (From Hinshaw et al. 2007, courtesy of the WMAP Science Team)Are there larger and better-known triangles in the universe? Yes, the CMB provides atool to measure giant triangles in the sky. The ancient radiation exhibits tiny deviationsfrom perfect uniformity produced by density and velocity perturbations in the primevalplasma. Since the first detection of these anisotropies, observed at a level δT/T ∼ = 10 −5by the differential microwave radiometer on board the Cosmic Background Explorer(COBE) satellite (Smoot et al. 1992), a number of experiments from ground and balloonhave been obtained, culminating with the Wilkinson Microwave Anisotropy Probe(WMAP) satellite mission. 13 The statistics of the anisotropies are described by a powerspectrum that shows an oscillating pattern as a function of angular scale (Fig. 9.1). Theso-called acoustic peaks in the power spectrum are the result of oscillating sound wavesin the photon-baryon fluid, a sort of primordial music of the forming cosmos (Hu andWhite 2004). This behavior is predicted by theory and provides evidence of a coherentonset of the initial fluctuations as expected in inflationary cosmologies (Guth 1997).The angular scale of the first peak corresponds to the angular size of the causal horizonat the last scattering surface. The giant cosmic triangles we need to measure spacecurvature are defined by our distance to the last scattering surface and by the length ofthe causal horizon at last scattering. Indeed, these are the largest causally connectedtriangles in the universe!13 The three-year results of WMAP were released in March 2006 (see Hinshaw et al. 2007).