Chapter 1 Introduction This thesis deals with a theory of the very early universe, called inflation theory. It focuses especially on how inflation can produce the seeds for the large-scale structures (galaxies and clusters of galaxies) that we see in our present universe. The first three sections of this chapter provide a general introduction to cosmology. The first section discusses the Big Bang theory, which describes the evolution of the universe. The second discusses the problems in this standard Big Bang theory and introduces a period of inflation as a possible solution to some of them. The third section gives an introduction on the cosmic microwave background radiation, observations of which are very important as they provide information about the early universe and inflation. Section 1.4 gives a detailed outline of the further contents of this thesis. This first chapter is meant for a broader audience and does not contain any formulae. More information on the general cosmology discussed here can be found in a number of textbooks, among others [176, 100, 149, 32, 151]. 1.1 TheBigBangtheory For a long time people have been looking up at the sky and trying to observe all the fas- cinating objects and phenomena that exist away from our own planet. With the progress of technology it has become possible to make more and more accurate observations, in- creasing our knowledge and understanding of the universe, but also creating new puzzles. Presently our picture of the universe looks as follows. At the smallest scales we find our solar system, with the sun, the nine planets and many moons, asteroids and comets. Our solar system is part of the Milky Way galaxy, which consists of hundreds of billions (1011) of stars. The Milky Way is part of the Local Group of galaxies, which contains about 30 galaxies, among them the Andromeda galaxy (M31) and the Large and Small Magellanic Clouds. This is an example of a (rather small) cluster of galaxies. This cluster, in its turn, is part of the Virgo supercluster, which is centered around the Virgo cluster and contains thousands of galaxies. The whole visible universe contains very many superclusters, which seem to be organized in a filamentary structure (like the Great Wall), with large voids in between. To give some indication of the sizes and distances involved, let us give some numbers. The unit of distance used in astronomy is the parsec.1 It is approximately the distance 11pc=3.086 · 1016 m = 3.26 lightyear (a lightyear is the distance light travels in one year). 8 Chapter 1. Introduction from the Sun to its nearest neighbour stars, which is about a hundred thousand times larger than the distance from the Earth to the Sun. The distance to the centre of the Milky Way is of the order of ten thousand parsec, while the distance to the Andromeda galaxy is approximately one million parsec (1 Mpc). The centre of the Virgo supercluster is at a distance of about 20 Mpc, and structures like the Great Wall have sizes of the order of a hundred megaparsec. Finally the size of the whole observable universe is of the order of ten thousand Mpc (10 Gpc). Although this means that there is a lot of structure at different scales, at the very largest scales observations show the universe to be very isotropic, i.e. the spatial distribu- tion of matter is on average the same in all directions. Unfortunately we can only make observations from our one planet in the universe. To be able to draw more general con- clusions from these observations, there is a common assumption called the cosmological principle, which states that our spatial position in the universe is in no way exceptional. Then one can draw the conclusion that the universe must be isotropic as seen from any point in space. Or, in other words, the universe considered at one time must be homoge- neous at large scales. Universe models that are spatially homogeneous and isotropic are called Friedmann-Robertson-Walker universes and they are described in section 2.1. One of the essential characteristics of cosmological observations is that because of the finite speed of light one automatically looks back in time when looking out into space. If we assume that the universe evolves in time, this means that our observations become influenced by evolutionary effects. And indeed these effects are observed, for example at the largest distances we find more quasars (an abbreviation of quasi-stellar object, origi- nally quasi-stellar radio source), which are probably galaxies in the process of formation. The fact that we observe evolutionary effects is a point in favour of the Big Bang theory, whose main characteristic is that the universe evolves. The principal observational ingredient of the Big Bang theory is the discovery by E. Hubble in 1929 [80] that all galaxies recede from our galaxy according to a simple law. This law, known as Hubble’s law, states that the recession velocity of a galaxy is proportional to its distance, the constant of proportionality being Hubble’s constant H0 with a value of approximately 70 km/s Mpc−1 (a more exact value can be found in table 1.1).2 Combining Hubble’s law with the cosmological principle leads to the important conclusion that the universe is expanding. A well-known analogue is the raisin pudding: a pudding with raisins randomly scattered through it, which swells steadily. The raisins represent clusters of galaxies, which do not expand themselves because of the gravitational attraction. As seen from one raisin all other raisins recede, and the raisin recession velocity increases with distance. Because of the expansion light from other galaxies is redshifted to lower frequencies, so that a certain distance corresponds with a certain redshift. If we extrapolate this expansion back in time, we find that the universe becomes smaller and smaller and the density and temperature become progressively higher. If the extrapolation is valid, one finally arrives at a singularity: the universe is just a point and the density and temperature are infinite. This singularity is called the Big Bang and this extrapolated time is chosen as the zero point of the time scale, t = 0. The standard Big Bang theory is a theory which takes the Big Bang as a starting point and gives a model for the further evolution of the universe based on the physics at high energies as we know it. 2Superimposed upon this Hubble velocity the galaxies have their own velocities of the order of 100 km/s caused by gravitational attraction within clusters and superclusters. This only changes the Hubble velocity appreciably for nearby galaxies, but it is the reason that the Andromeda galaxy does not recede from our galaxy but approaches it. 1.1. The Big Bang theory 9 Cosmological quantity Symbol Value −1 −18 −1 Hubble constant H0 72 ± 8km/sMpc (= 2.3 · 10 s ) Temperature of CMBR T0 2.725 ± 0.001 K 17 Age of universe t0 13.4 ± 1.6Gyr(=4.23 · 10 s) +1.3 −5 Radiation density parameter Ωr 4.8−0.9 · 10 Baryonic matter Ωb 0.04 ± 0.01 Total matter Ωm 0.3 ± 0.1 Dark energy ΩΛ 0.7 ± 0.1 Total density parameter Ωtot 1.00 ± 0.06 Table 1.1: Present values of a number of cosmological parameters, according to [123]. This means that at energies per particle exceeding 100 GeV the standard Big Bang theory in essence only extrapolates known physics, since we cannot yet make measurements at such high energies. An example of a potential ‘new’ physical process at higher energies, which is not included in the standard Big Bang theory, is inflation, see section 1.2. Although the history of the universe according to the standard Big Bang theory is described below, we now single out two aspects that played a crucial role in observa- tionally confirming the Big Bang theory. These are the cosmic microwave background radiation (CMBR) and nucleosynthesis. According to the Big Bang scenario the universe was very hot at early times, so that many photons with a high temperature were pro- duced. These photons should still be around, although with a much lower temperature because the expansion of the universe increases their wavelengths to larger values, which corresponds with a lower frequency or energy (this is called redshift). And indeed this CMBR with a temperature of about 3 K was first measured in 1965. The CMBR is dis- cussed more thoroughly in section 1.3. Another consequence of a hot early universe is that nuclear reactions should have caused the formation of some light elements besides hydrogen, in particular deuterium and helium. This is called nucleosynthesis, and indeed observations of deuterium and helium abundances agree with predictions from Big Bang nucleosynthesis. (The homogeneous distribution of helium points to a cosmological origin anyway, as opposed to formation in stars, while deuterium is only destroyed by stars.) Regarding the matter (and more exotic forms of energy) content of the universe, ob- servations have led to the picture given in table 1.1. The energy densities of the various components are given relative to the critical density of the universe, in the form of the so-called density parameters Ωi (in other words, Ωi = ρi/ρc,whereρi is the energy den- sity of component i and ρc is the critical density of the universe; see section 2.1 for more information). For a spatially flat universe the total energy density by definition equals the critical density, so that Ωtot = 1. An equivalent statement is that the curvature density parameter ΩK =Ωtot − 1 is zero.