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In this ﬁnal chapter, we review three experimental predictions of the cosmological model that we developed in chapter 9, and their observational veriﬁcation. The tests are cosmo- logical redshift (in the context of distances to type-Ia supernovae, and baryon acoustic oscillations), the cosmic microwave background, and nucleosynthesis of the light ele- ments. Each of these tests also provides information on the particular parameters that describe our Universe. We conclude with a brief discussion on the use of quasars and other distant objects as cosmological probes.
10.1 Cosmological Redshift and Hubble's Law
Consider light from a galaxy at a comoving radial coordinate re. Two wavefronts, emitted at times te and te + te, arrive at Earth at times t0 and t0 + t0, respectively. As already noted in chapter 4.5 in the context of black holes, the metric of spacetime dictates the trajectories of particles and radiation. Light, in particular, follows a null geodesic with ds = 0. Thus, for a photon propagating in the FLRW metric (see also chapter 9, Problems 1–3), we can write
dr2 0 = c2dt2 − R(t)2 . (10.1) 1 − kr2
The ﬁrst wavefront therefore obeys t0 dt 1 re dr = √ , (10.2) − 2 te R(t) c 0 1 kr and the second wavefront