This book is devoted to a systematic discussion of the physics of the cosmic microwave background. This field of physics is very complex and involves an enormous diversity of processes that occur in the course of expansion of the Universe. The CMB proved to be a true ‘goldmine’ for extracting scientific information on these processes; it has in fact grown into the central branch of modern cosmology. Comparing this highly perfected theory with observational data makes it possible to obtain essential information on the early Universe and on the physical parameters of the Universe as a whole.

Combining these results with results from other branches of astrophysics, such as the large-scale structure of the Universe, supernovae, etc., provides a robust basis of modern cosmology.

Results from BOOMERANG, MAXIMA-1, ARCHEOPS, CBI, DASI and WMAP were so important that they have taken the field into the era of ‘precision cosmology’. As we have discussed, these studies have produced impressive constraints on many fundamental cosmic parameters and have led to a very definite picture of the structure and evolution of the Universe. As a result, one could become overexcited and declare that almost everything in cosmology is now known. However, we want to emphasize that even after those remarkable projects, the study of CMB physics is not coming to an end. There are still many unsolved problems in cosmology, and another generation of satellite experiments, as well as ground-based and balloon-borne experiments, is needed.

Introduction

The completion of the recent balloon experiments BOOMERANG, MAXIMA-1, TOP-HAT and ground-based experiments DASI, CBI and VSA ushered in a new phase in the experimental investigation of anisotropy and polarization of the cosmic microwave background. The satellite WMAP, launched successfully in June 2001, opened a new era in the study of the CMB anisotropy and polarization, which differs from previous experiments in its greater accuracy of finding the characteristics of the cosmological signal, and hence of the cosmological parameters. We mean here the Hubble constant H0, the density Ωb of the baryonic fraction of matter in the Universe, the hidden mass density Ωdm, the dark energy density ΩΛ (the vacuum?), the exponent n in the spectrum of adiabatic perturbations, and a number of others.

An international satellite, PLANCK, whose aim is to measure anisotropy and polarization of the primordial radiation with unprecedented accuracy is scheduled for launch in 2007. The accepted opinion is that PLANCK will summarize more than 35 years of progress in the theoretical and experimental study of polarization and anisotropy of the CMB and will allow us to come very close to building a realistic model of the Universe.

Before discussing the main features contributed by WMAP and PLANCK, we briefly sum up the results achieved by radioastronomy and cosmology in studying the CMB anisotropy.

Introduction

In a way, the entire history of cosmology from Ptolemy and Aristotle to the present day can be divided into two stages: a period before and a period after the discovery of the cosmic microwave background (CMB). The first period was the subject of hundreds of volumes of literature; now it is not only an integral part of science, but also marks a step in the progress of mankind. The second stage started in 1965 when two American researchers, A. Penzias and R. Wilson published their famous article in the Astrophysical Journal, ‘A measurement of excess antenna temperature at 4080 Mc/s’ (Penzias and Wilson, 1965), in which they announced the discovery of a previously unknown background radio noise in the Universe. Another article, in the same issue of the Astrophysical Journal, preceded the one by Penzias and Wilson; this was by R. Dicke, P. J. E. Peebles, P. Roll and D. Wilkinson (Dicke et al., 1965) and discussed the preparation of a similar experiment at a different wavelength, but also interpreted the Penzias–Wilson results as confirming the predictions of the ‘hot universe’ theory. The radiation with a temperature close to 3 K discovered by Penzias and Wilson was described as the remnant of the hot plasma that existed at the very onset of expansion which then cooled down as a result of expansion.

Introduction

In this chapter we concentrate on testing the statistical properties of anisotropy and polarization fields generated by primary perturbations of density, velocity and gravitational potential in the hydrogen recombination epoch. The main working hypothesis on which both the modern theory of structure formation in the Universe and the theory of generation of primordial anisotropy and polarization are based is the assumption of the random nature of the distribution of values of amplitude and phase of the primordial perturbations.

We need to emphasize that the idea of the random nature of primordial perturbations was introduced into cosmology long before it was ultimately explained in terms of inflationary models. In a certain sense, this idea reflects the fact that the distribution of matter in the Universe on spatial scales exceeding 102 Mpc is on average uniform and isotropic. If the formation of structures in different parts of the Universe separated by distances greater than 102–103 Mpc occurred independently of one another, it is then only natural to assume that the primordial distributions of the density, velocity and gravitational potential perturbations were once equally independent. Moreover, we know that non-linear in amplitude perturbations of density resulting from condensation of matter on smaller scales also evolved from small fluctuations.

Introduction

The subject of this chapter is an analysis of one of the most impressive predictions of the modern theory of the structure and evolution of the Universe: the prediction of angular anisotropy in the temperature distribution of the cosmic microwave background on the celestial sphere; we will also analyse observations of this phenomenon. This anisotropy results from the interaction of the primordial radiation background with perturbations of density and velocity of the baryonic matter and with perturbations of the metric; these make an inseparable part of any scenario of structure formation in the expanding Universe. We also use this introductory section to share our personal recollections of the period when the theory of anisotropy of the CMB was being created and the first attempts were being made to detect it by observations. These notes are quite subjective and do not attempt to provide historical analysis. We hope nevertheless that the reader will find them interesting. We wish to point out first of all that while the microwave background itself was discovered by accident, its anisotropy was discovered as a result of well-planned observational searches based on a carefully developed theory.

One of the present authors (I. Novikov) was there at the moment of inception of this field of astrophysics – nowadays a fully-fledged field – and remembers well the history of conception of the theory and the drama of the experimental attempts to detect the anisotropy of primordial radiation at the end of the 1960s and the beginning of the 1970s.

The English translation of our book appears three years after the first Russian edition, which was published in 2003. Cosmology, and specifically the cosmology of the cosmic microwave background (CMB), is the most rapidly evolving branch of science in our time, so there have been several important advances since the first edition of this book. Some extremely important developments – the publication of new observational results (particularly the observations of the Wilkinson Microwave Anisotropy Probe (WMAP) space mission), the discussion of these results in numerous papers, the formulation of new ideas on the physics of the CMB, and the creation of new mathematical and statistical methods for analysing CMB observations – have arisen since the completion of the Russian edition, originally entitled Relic Radiation of the Universe. The term ‘cosmic microwave background’ used in publications in the West (and now often in Russia) is rather clumsy. ‘Relic radiation’, introduced by the Russian astronomer I. S. Shklovskii, is an impressive name that appealed to many astrophysicists; however, since CMB is used in the specific literature in the field, we had to call the English version of our book The Physics of the Cosmic Microwave Background, and we continue using this term throughout the book.

In the original Russian edition, we tried to give a complete review of all the important topics in CMB physics.

We wrote this book in 2001–2002. These years saw the launch and start of operations of the American satellite WMAP (Wilkinson Microwave Anisotropy Probe), which began a new stage in the study of the primordial electromagnetic radiation in the Universe. This stage brought a qualitative change to the status of modern cosmology which, using a metaphor suggested by Malcolm Longair, entered the phase of ‘precision cosmology’ in which the level of progress in theory and experiment was so high that the interpretation of observational data became relatively less urgent than the problem of measuring the most important parameters that characterize the state of gravitation and matter as they were long before the current phase of the cosmological expansion.

Paradoxically, the entire period of explosive development of cosmology happened virtually within the last three decades of the twentieth century; however, it brought together thousands of years of mankind's attempts to comprehend the basic laws governing the structure and evolution of the Universe. Regarded formally, this period coincided – although realistically it was genetically connected – on one hand with the penetration into the mysteries of structure of matter at the microscopic level and on the other hand with the sending of humans into space and with progress in space technologies that revolutionized the experimental basis of the observational astrophysics.

Mission and instrument

The successful launch of the WMAP (Wilkinson Microwave Anisotropy Probe) mission in June 2001 signalled a new epoch in the investigation of the cosmic microwave background. This experiment differs from all previous satellite-, balloon- and ground-based experiments by unprecedented precision and sensitivity.

The WMAP mission has been designed to determine the power spectrum of the CMB anisotropy and polarization and subsequently to estimate such cosmological parameters as the Hubble constant H0, the baryonic fraction of dark matter Ωb, the geometry ΩK of the Universe, etc. These observations provide an independent check on the COBE results, determine whether the anisotropy obeys Gaussian statistics, and verify whether the predicted temperature–polarization correlation is present.

The high-level features of the WMAP mission can be briefly described as follows. The mission is designed to produce an almost full (>95% of the entire sky) map of the CMB temperature fluctuations with ≃0.2° angular resolution, accuracy on all angular scales >0.2°, accurate calibration (<0.5% uncertainty), an overall sensitivity level of ΔTrms < 20 μK per pixel (for 393 216 sky pixels, 3.2 × 10−5 ster per pixel) and systematic errors limited to <5% of the random variance on all angular scales.

We have taken information from Page (2000) to describe the instrument. The instrument measures temperature differences from two regions of the sky separated by ∼140°. It is composed of ten symmetric, passively cooled, dual-polarization differential microwave receivers.