Introduction

1 Introduction

The Universe started from a very hot, dense phase about 15 billion years ago in the Big Bang. The very early Universe was opaque due to the constant interchange of energy between matter and radiation. The Universe then cooled to a temperature of $∼$ 4000 K through its expansion about 300,000 years after the Big Bang. At this stage, the matter does not have sufficient energy to remain ionised. The electrons combine with the protons to form atoms, and the cross section for Compton scattering with photons is dramatically reduced. The radiation from this point in time has been traveling towards us for 15 billion years and has now cooled to a blackbody temperature of 2.7 degrees Kelvin. This is summarised in Figure 1 . At this temperature, the Planck spectrum has its peak at microwave frequencies ( $∼$ 1–1000 GHz), and its study forms a branch of astronomy called Cosmic Microwave Background astronomy (hereafter CMB astronomy). In 1965, Arno Penzias and Robert Wilson [68 ] were the first to detect this radiation. It is seen from all directions in the sky and is very uniform. This uniformity creates a problem. If the universe was so smooth, then how did anything form? There must have been some bumps in the early universe that could grow to create the structures we see today.

Figure 1: The thermal history of the Universe.

As the Universe grows older, the observable Universe gets bigger, due to the finite speed of light. The particle horizon of an observer is the distance to the farthest object that could have affected that observer. Any objects further than this point are not, and never have been, in causal contact with the observer. At the last scattering surface the particle horizon corresponds to $𝜃 ∼ 2∘$ as seen from Earth today. No physical processes will act on scales larger than this. At the epoch of recombination, fluctuations on scales larger than 2° must have been produced by matter perturbations already present at this time. It is thought these fluctuations were probably laid down only 10^–34 seconds after the big bang, and have their origin in quantum fluctuations of a scalar field. On smaller scales, corresponding to regions in causal contact at recombination, we should be able to see in the CMB the effects of physical processes occurring at recombination, such as acoustic oscillation of the coupled photon-baryon fluid, which thus also gives us a direct link with the physics of galaxy formation.

In 1992, the NASA Cosmic Microwave Background Explorer (COBE) satellite was the first experiment to detect the bumps [86 ]. These initial measurements were in the form of a statistical detection rather than individual physical features (Some features in the first year maps were real CMB anisotropies. but it was not possible to distinguish these from the noise except in a statistical way.). Today, experiments all around the world are finding these bumps, both causally connected and non-causally connected, that eventually grew into galaxies and clusters of galaxies. The required sensitivities called for new techniques in astronomy. The main principle behind all of these experiments is that, instead of measuring the actual brightness, they measure the difference in brightness between different regions of the sky. The experiments at Tenerife produced what was probably the first detection of the real, individual CMB fluctuations [33 ] on scales comparable to the beam size of the experiment. These particular features were later confirmed by the COBE two-year data [53 ].

There are many different theories of how the universe began its life and how it evolved into the structures seen today. Each of these theories make slightly different predictions of how the universe looked at the very early stages which up until now have been impossible to prove or disprove. Knowing the structure of the CMB, within a few years it should be possible for astronomers to tell us where the universe came from, how it developed and what will happen to it in the future.

Useful overall reviews of the physics of the production of CMB fluctuations, which will complement the informal presentation given in the next section, are contained in White et al., 1994 [97 ], Scott et al., 1995 [81 ] and Hu et al., 1995 [40 ]. This review is intended to be an extension and update of Lasenby and Jones, 1997 [51 ], and parts of that review are reproduced here so that the arguments are easily followed.