© Copyright, Princeton University Press. No part of this book may be distributed, posted, or reproduced in any form by digital or mechanical means without prior written permission of the publisher.
10 Tests and Probes of Big Bang Cosmology
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