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.

Why Riemannian geometry?

As argued in Section 1.4, gravitational forces can be simulated by inertial forces in accelerated motion. Special relativity describes relations between objects in uniform motion with respect to inertial frames, while gravitational interactions are neglected. The metric of the Minkowski spacetime in an inertial reference frame has constant coefficients. If we transform that metric to an accelerated frame, its components will become functions. Hence, a gravitational field should have the same effect: in a gravitational field the metric should also have non-constant components. Unlike in the Minkowski spacetime, in a gravitational field it should not be possible to make the metric components constant by a coordinate transformation. This was, in great abbreviation, the basic observation that led Einstein (1916) to general relativity.

This idea had to be supplemented with equations that would generalise the Newtonian laws of gravitation, and would relate the metric form to the gravitational field. The derivation of these equations, together with several related matters, will be presented in this chapter.

Local inertial frames

Let us recall the conclusion of Chapter 1: the Universe is permeated by gravitational fields that cannot be screened. Their intensity can be decreased by going away from the sources, but one can never decrease that intensity below the minimum determined by the local mean density of matter in the Universe. For this reason, no body in the Universe moves freely in the sense of Newton's mechanics, and consequently inertial frames can be realised only approximately, with a limited precision. Moreover, there exists no natural standard of a straight line, so the departures of real motions from rectilinearity cannot be measured.