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2.1. Evolution of the Energy Density in the Early Universe

The basic question addressed when investigating the history of the Universe as a whole in the framework of modern physics is the following: Why do we see something instead of detecting nothing? It originates from the common wisdom that any isolated system after long enough evolution will reach thermal equilibrium, characterized by a homogeneous structureless distribution of its energy. Nearly 14 billion years after the Big Bang, one observes the presence of complicated hierarchical structures on all scales, starting from the subnuclear world, through chemical elements, and up to the scale of galaxy clusters. This section will review our present understanding of how the structured evolution of the Universe could be sustained for a time more than 60 orders of magnitude longer than the characteristic timescale of the particle physics processes present at the moment of its 'birth.'

The information concerning the constitution of the early Universe has increased tremendously during the past decade, mainly due to improved observations of the cosmic microwave background radiation (CMBR). The most important cosmological parameters (the total energy density, the part contained in baryonic matter, the part of nonbaryonic dark matter (DM), other components, etc.) have been determined with percent level accuracy as a result of projects completed in the first decade of the twenty-first century and now appear in tables of fundamental physical data (Amsler et al. 2008).

Observations of CMBR

The existence of CMBR was predicted by Alpher et al. (1948) as a direct consequence of the Hot Big Bang Universe of Gamow (Lamarre and Puget 2001). It was discovered by Penzias and Wilson (1965). It originates from the combination of the once free electrons and protons into neutral atoms when the temperature of the Universe dropped below kT = 13.6 eV (the ionization energy of the H-atom, i.e., T = 1.58 × 105 K) to nearly 1 eV (1.16 × 104 K). (Note that in certain branches of physics it is customary to express temperature in eV units through the equation E = kT. The conversion is given by 1 eV corresponds to 1.16045 × 104 K.) After the recombination, the Universe became transparent to this radiation, which at present reaches the detectors with a redshift determined by the kinematics of the expansion of the Universe (Lamarre and Puget 2001). It appears to be a perfect thermal radiation with Planckian power distribution over more than three decimal orders of magnitude of frequency, having a temperature of T = 2.725 ± 0.001 K.

The first quantitative evidence for the temperature anisotropy of CMBR was provided by the COBE (Cosmic Background Explorer) satellite in 1992. The angular resolution of its detectors was 7°. This enabled the collaboration to determine the first 20 multipole moments of the fluctuating part of CMBR beyond its isotropic component. It has been established that the degree of anisotropy of CMBR is one part in one hundred thousand (10−5). There are two questions of extreme importance related to this anisotropy:

  1. Is this anisotropy the origin of the hierarchical structure one observes today in the Universe?
  2. What is the (micro)physical process behind this anisotropy?

Section 2.4 returns to the answer to the first question. To the second question, the answer will be briefly outlined below.

Following the success of the COBE mission several more refined (ground based and balloon) measurements of the CMBR fluctuations were performed between 1998 and 2001. An angular resolution of about 1° has been achieved, which was further refined to the arc-minute level by the satellite mission Wilkinson Microwave Anisotropy Probe (WMAP). The combined efforts of these investigations allowed the determination of the multipole projection of CMBR on the sky up to angular moments l = 2,000. The fluctuation information extracted until 2007 is presented in Fig. 1 with lmax = 2,000. One easily recognizes the presence of three pronounced maxima in this figure (possible additional, weaker maxima are discussed further below).

Figure 1

Figure 1. Multipole fluctuation strength of the cosmic microwave background radiation as a function of the spherical harmonic index l. The location and the height of the first minimum favors a spatially flat Universe, while the level of the fluctuations in the higher multipoles (l > 400) indicates the presence of a low-density baryonic component (< 5%). The measurements cover already the damping region (l > 1,000). Wilkinson Microwave Anisotropy Probe (WMAP) data are displayed together with results of earlier balloon observations (Reprinted from Nolta et al. 2009 with kind permission of the first author, the WMAP Science Team, and AAS)

Another important characteristic of the CMBR anisotropy is its spectral power distribution. The measured distribution is nearly scale invariant; it is the so-called Zel'dovich–Harrison spectrum (see Peebles 1993). This means that every unit in the logarithm of the wave number contributes almost equally to the total power.

The small-amplitude and almost scale-invariant nature of the fluctuation spectra, described above, reflects the very early fluctuations of the gravitational field. First of all, one has to emphasize that the coupled electron–proton–photon plasma near recombination was oscillating in a varying gravitational field (Hu 2001). Where the energy density was higher the plasma experienced the effect of a potential well, and the radiation emerging from this region was hotter than average. On the contrary, diminutions of the energy density led to a colder emission. Still, an observer located far from the sources detects lower temperature from denser sources due to the Sachs–Wolfe effect (Peebles 1993). In any case, the CMBR anisotropy actually traces the inhomogeneity of the gravitational potential (or total energy density) in the era of recombination.

Thomson scattering of the anisotropic CMBR on the ionized hot matter of galaxy clusters and galaxies results in roughly 5% linear polarization of CMBR. Its presence in CMBR was first detected by the Degree Angular Scale Interferometer (DASI) experiment (Kovac et al. 2002). Starting from 2003, the WMAP experiment also measured the temperature–polarization cross correlation jointly with the temperature–temperature correlation. The significance of this type of measurement is obvious since the presence of ionized gases corresponds to the beginning of the epoch of star formation.

Inflationary Interpretation of the CMBR

A unique particle physics framework has been proposed, which can account for the energy density fluctuations with the characteristics found in CMBR. One conjectures that the large-scale homogeneity of the Universe is due to a very early period of exponential inflation in its scale (Peebles 1993).

One assumes that during the first era after the Big Bang the size of the causally connected regions (the horizon) remained constant, while the global scale of the Universe increased exponentially. This is called inflationary epoch. The wavelength of any physical object is redshifted in proportion with the global scale. Therefore, at a certain moment, fluctuations with a wavelength bigger than the horizon were "felt" as constant fields and did not influence anymore the gravitational evolution of the matter and radiation at smaller length scale.

The inflationary period in the evolution of the Universe ended at about 10−32 s after the Big Bang. At this moment, the constant ordered potential energy density driving the inflation decayed into the particles observed today. Some of them may have belonged to a more exotic class, which can contribute to the violation of the matter–antimatter symmetry if they exhibit sufficiently long lifetimes (see Sect. 2.2). The rate of expansion of the horizon in the subsequent radiation- and matter-dominated eras was always faster than the global expansion of the Universe (see Fig. 2). Radiation-dominated means that the main contribution to the energy density comes from massless and nearly massless particles with much lower rest energy than the actual average kinetic energy. Therefore, the long-wavelength fluctuations having left during inflation continuously reentered the horizon and their gravitational action was "felt" again by the plasma oscillations. The first maximum of the CMBR multipole moments corresponds to the largest wavelength fluctuations that were just entering the horizon in the moment of the emission of CMBR.

Figure 2

Figure 2. Variation of the characteristic length scales during the history of the Universe. On both axes the logarithm of the corresponding length is measured. The wavelengths of physical phenomena (full lines) grow linearly with the scale parameter of the Universe. The size of the causally connected domains (dot-dashed line) stagnates during the exponential growth (inflation), whereas it increases faster than the length scale of the Universe later, i.e., quadratically in the radiation era and with 3/2 power under matter domination.

Since during its evolution beyond the horizon, any dynamical change in the fluctuation spectra was causally forbidden, the fluctuating gravitational field experienced by the recombining hydrogen atoms was directly related to the fluctuation spectra of the inflationary epoch, determined by the quantum fluctuations of the field(s) of that era. This observation leads promptly to the conclusion that the spectra should be very close to the Zel'dovich–Harrison spectra. Detailed features of the power spectra seem to effectively rule out some of the concurrent inflationary models.

Also the simplest version of the field-theoretical realization of inflation predicts a total energy density very close to the critical density ρc, which separates the parameter region of a recollapsing Universe from the region where a non-accelerating expansion continues forever. Such a Universe is spatially flat. In the apparently relevant case of accelerated expansion, the borderline is shifted and universes somewhat above the critical densities might expand with no return. It is customary to measure the density of a specific constituent of the Universe in proportion to the critical density: Ωi = ρi / ρc.

An important prediction of the inflationary scenario for the origin of CMBR anisotropy is a sequence of maxima in the multipole spectrum (Hu 2001). The latest results (see Fig. 1) confirm the existence of at least two further maxima, in addition to the main maximum known before. The new satellite-based CMBR observations by the European satellite PLANCK launched in May 2009 will improve the accuracy of the deduced cosmological parameters to 0.5% and determine the multipole projection of the anisotropy up to angular momentum l ∼ 2,500.

The positions and the relative heights of these maxima allow the determination of the relative density of baryonic constituents among the energy carriers. The increased level of accuracy leads to the conclusion that the baryonic matter (building up also the nuclei of all chemical elements) constitutes no more than 5% of the energy content of the Universe. This conclusion agrees very convincingly with the results of the investigation of the primordial abundance of the light chemical elements to be described in detail in Sect. 3. These facts lead us to the unavoidable conclusion that about 95% of the energy content of the Universe is carried by some sort of nonbaryonic matter. (More accurate numbers will be given at the end of this section). The discovery of its constituents and the exploration of its extremely weak interaction with ordinary matter is one of the greatest challenges for the scientific research in the twenty-first century.

Dark Matter: Indications, Candidates, and Signals

Beyond CMBR, growing evidence is gathered on a very wide scale for the existence of an unknown massive constituent of galaxies and galaxy clusters. It is tempting to follow a unified approach describing the "missing gravitating mass" from the galactic to cosmological scale (i.e., from a few tens of kpc to Mpc, with 1 pc = 3.26 light-years = 3.0856 × 1013 km). In this subsection the main evidence already found and the ongoing experimental particle physics efforts for direct detection of the dark matter (DM) constituents are shortly reviewed.

First hints of some sort of gravitating Dark Matter below the cosmological scale came from galactic rotation curves (some tens of kpc), then from gravitational lensing (up to 200 kpc), and from the existence of hot gas in galaxy clusters. The anomalous flattening of the rotation curves of galaxies was discovered in the 1970s. Following Kepler's law, one expects a decrease of the orbiting velocity of all objects (stars as well as gas particles) with increasing distance from the galactic center. Instead, without exception a tendency for saturation in the velocity of bright objects in all studied galaxies is observed. The simplest explanation is the existence of an enormous dark matter halo. Since velocity measurements are based on the 21 cm hydrogen hyperfine radiation, they cannot trace the galactic gravitational potential farther than a few tens of kiloparsecs. Therefore, with this technique only the rise of the galactic dark matter (DM) haloes can be detected but one cannot find their extension.

Dark supermassive objects of galactic cluster size are observable by the lensing effect exerted on the light of farther objects located along their line of sight. According to general relativity the light of distant bright objects (galaxies, quasars,gamma ray bursts(GRBs)) will be bent by massive matter located between the light source and the observer along the line of sight. Multiple and/or distorted images arise, which allow an estimate of the lensing mass. The magnitude of this effect, as measured in the Milky Way, requires even more DM out to larger distances than it was called for by the rotation curves (Adelmann-McCarthy et al. 2006).

The large-scale geometry of the galactic DM profile semiquantitatively agrees with results of Newtonian many-body simulations, though there are definite discrepancies between the simulated and observed gravitating densities at shorter distances. Interesting propositions were put forward by Milgrom to cure the shorter-scale deviations with a modified Newtonian dynamics (MOND) (reviewed by Milgrom 2008).

Gravitational lensing combined with X-ray astronomy can trace the separation of bright and dark matter, occurring when two smaller galaxies collide. The motion of the radiating matter is slowed down more than that of the DM components. As a consequence, the centers of the lensing and X-ray images are shifted relative to each other. A recent picture taken by the Chandra X-ray Telescope is considered as the first direct evidence for the existence of DM on the scale of galaxy clusters (Clowe et al. 2006).

Another way to estimate the strength of the gravitational potential in the bulk of large galaxy clusters is offered by measuring spectroscopically the average kinetic energy (e.g., the temperature) of the gas. One can relate the very high temperature values (about 108 K) to the depth of the gravitational potential assuming the validity of the virial theorem for the motion of the intergalactic gas particles. Without the DM contribution to the binding potential the hot gas would have evaporated long ago.

Three most popular DM candidates could contribute to the explanation of the above wealth of observations. Historically, faint stars/planetary objects constituted of baryonic matter were invoked first, with masses smaller than 0.1 solar mass (this is the mass limit minimally needed for nuclear burning and the subsequent electromagnetic radiation). The search for massive compact halo objects (MACHOs) was initiated in the early 1990s based on the so-called microlensing effect – a temporary variation of the brightness of a star when a MACHO crosses the line of sight between the star and the observer. This effect is sensitive to all kind of dark matter, baryonic or nonbaryonic. The very conservative combined conclusion from these observations and some theoretical considerations is that at most 20% of the galactic halo can be made up of stellar remnants (Alcock et al. 2000).

Complementary to this astronomy-based proposition elementary particle physics suggests two distinct nonbaryonic "species", which originate from the extreme hot period of the Universe and therefore could be present nearly homogeneously on all scales. Axions are hypothetical particles of small (10–(3–6) eV/c2) rest energy. They were introduced (Peccei and Quinn 1977) for the theoretical explanation of the strict validity of the symmetry of strong interactions (QCD) under the combined application of space- and charge reflections (CP-invariance). Although they are very light, their kinetic energy is negligible, since they are produced in nonthermal processes. This way they represent the class of cold dark matter. The parameter space was and is thoroughly searched for axions in all particle physics experiments of the last 2 decades. The presently allowed mass range is close to the limit of the astrophysical significance of these particles.

The most natural DM candidates from particle physics are weakly interacting massive particles (WIMPs). Assuming that the thermal abundance of the WIMPs is determined by the annihilation and pair-production processes with themselves, one can estimate their present density as a function of the annihilation cross section. It is quite remarkable (even qualified sometimes as "WIMP miracle") that, using cross sections typical of the supersymmetric extension of the standard particle physics model, just the gravitating density missing on the cosmological scale is found. By this coincidence, one identifies WIMPs with the lightest stable supersymmetric particle (called neutralino). The neutralino's mass is on the scale of heavy nuclei; usually one assumes it to equal the mass of the tungsten atom. It would constitute pressureless cold dark matter, with a density calculable by analyzing its decoupling from thermal equilibrium.

An important milestone in the WIMP-story will be reached once the Large Hadron Collider (LHC) at CERN begins working. The available energy covers the expected mass range of the most popular variants of supersymmetric extensions. Currently, extensive strategies are worked out for the identification of prospective new massive particles to be observed at LHC, along with their cosmologically motivated counterparts (Baltz et al. 2006).

A positive identification at CERN would give new impetus to the underground direct searches for WIMPs. Such research is based on looking for heat deposition by particles arriving from the nearest galactic neighborhood into cryogenic detectors, well isolated from any other type of heat exchange. At present, only a single such experiment, i.e., the Dark Matter (DAMA) experiment in Gran Sasso, Italy, has reported a positive signal in the DM particle search. For more than 5 years now, a seasonal variation in the heat deposition rate is observed, which may be caused by the DM particle flux variation along the orbit of the Earth (Bernabei et al. 2003).

Although the analysis of CMBR excludes the domination of hot dark matter, i.e., relativistic weakly interacting particles, like light neutrinos, there still exists a plethora of more exotic propositions for the constituents of dark matter, not yet accessible for experimental verification, like primordial black holes, nonthermal WIMPzillas, and the so-called Kaluza–Klein excitations of higher-dimensional theories.

Dark Energy, the Accelerating Universe, and the Problem of Distance Measurements

The expansion of the Universe is conventionally characterized by the Hubble law, stating that cosmological objects uniformly recede from the observer with a velocity proportional to their distance. The proportionality factor H has not remained constant during the evolution of the Universe, the rate of change being characterized by the deceleration parameter q0 = dH–1 / dt – 1 (Peebles 1993).

The deceleration can be probed by distance measurements using type Ia supernovae. As explained in Sect. 5.3 these very energetic cosmic events occur in a rather narrow mass range of compact objects, with a minimal scatter in their energy output or luminosity L, which determines also the energy flux F reaching the observer at distance dL called luminosity distance. Therefore, type Ia supernovae are standardizable light sources (standard candles), their light curves can be transformed into a universal form.

Standard candles are important tools to measure astronomical distances. Knowing the luminosity (i.e., energy output) of an object, it is straightforward to calculate its distance by the observed brightness, which drops with the inverse square of the distance 1 / r2. The advantage of using SN Ia is that they are outshining all the stars in a regular galaxy and thus can be seen and studied over vast distances.

More recently, the method of measuring distances with SN Ia has acquired some fame by showing that the Universe is expanding faster at large distances than expected by the standard cosmological model (Perlmutter et al. 1999; Riess et al. 1998; Leibundgut 2001a, b).

The luminosities of 42 SN Ia were analyzed in these pioneering publications as a function of their redshift. The survey comprised objects with redshift z ≤ 1, which corresponds to an age ≤ 10 Ga (gigayears). Assuming that the absolute magnitude of these objects is independent of the distance (excluding evolution effects) the apparent luminosities were detected on an average 60% fainter than expected in a Universe, whose energy density is dominated by nonrelativistic matter. A number of data points with z ≤ 0.7 are displayed in Fig. 3, all having positive deviation for the difference of the apparent and absolute luminosities, m – M (note that the fainter is a source the larger is its magnitude). The simplest interpretation is to assume the scattering of the light on its way from the source by some sort of "dust" (full line) leading to objects that are fainter than foreseen. A less conventional interpretation is to assume positive acceleration of the global expansion. (An accelerating source is located farther away, and will appear to be fainter at a certain z than expected in standard cosmology.)

Figure 3

Figure 3. Variation of the difference of the observed (m) and absolute (M) luminosity for the SN Ia with redshift z, measured in a special astronomical unit, called magnitude. The zero level corresponds to supernovae in an empty (Ω = 0) Universe. A positive difference signals sources that are fainter than expected. A brighter (negative) value is naturally interpreted as the decelerating action of the gravitational force exerted on the source by a nonzero rest energy (ΩM ≠ 0). See text for models corresponding to the different curves possibly producing positive values (Reprinted from Riess et al. 2001 with kind permission of the first author and AAS)

The quantitative argument is based on relating the measurements to the deceleration parameter defined above. In fact the luminosity distance of an object at redshift z can be expressed as an integral of an expression of the varying Hubble-parameter H(z) on the interval (0, z), where z = 0 corresponds to the observer's position today. When the redshift is not too large, one can expand this integral into a series of z and arrive in the first approximation at a simple linear relation expressing Hubble's law of the dependence of the luminosity distance on the redshift. Its first nonlinear correction involves the deceleration parameter: dL = (c / H0) z [1 + (1 - q0) z / 2 + ...]. Dust absorption diminishes the source brightness irrespective of the value of z. On the other hand, the presence of both matter and a cosmological constant will change the sign of the deceleration parameter with z.

In the past decade several projects contributed to the luminosity distance measurements and by now (i.e., as of 2009) the list includes over 200 events. Specifically with the help of the Hubble telescope 13 new Sn Ia were found with spectroscopically confirmed redshifts exceeding z = 1 and at present the full sample contains already 23 z > 1 objects (Riess et al. 2007). Such objects most strongly influence the value of the deceleration parameter. A combined analysis of all Sn Ia data yields a deceleration parameter value of -0.7 ± 0.1 (Kowalski et al. 2008). Its negative value signals an accelerating expansion rate at distance scales comparable to the size of the Universe.

A nonzero cosmological constant Λ in the equations describing the dynamics of the Universe can account for such an acceleration. The cosmological constant is related to a vacuum energy density (ρ) characterized by negative pressure (equation of state p = w ρ, with w = -1). Nowadays, the more general term 'dark energy' is used for the hypothetical agent of such an accelerating effect (acceleration requires w < -1/3).

The fraction of the total energy density stored in Λ is not constant in time. Although Λ is constant by definition, the energy densities in the radiation and matter components are varying respectively as quartic and cubic inverse powers of the distance scale of the Universe. The early Universe until the decoupling of the photons is radiation-dominated and the Λ energy density is negligible. Initially, the matter density (including nonbaryonic dark matter) is dominating after decoupling, exerting a conventional decelerating effect on the motion of cosmological objects. Because of the reduction of the matter density with the expansion of the Universe, its contribution to the total energy density (and total Ω = ΩM + ΩΛ) may become smaller than the one of Λ at a given point in time. How early this crossover happens depends on the absolute value of Λ, which is not constrained by any current theory. From this point of view, it is remarkable that ΩM and ΩΛ are of the same order of magnitude in the Universe at present. Because of this and the rather small value of Λ its impact on the cosmic expansion can only be detected over large distances, i.e., when studying distances of objects with large redshift z. In the distant future, the repulsive action of a nonzero Λ will more and more dominate. Without any additional effect, this leads to a 'Big Rip' scenario in which smaller and smaller volumes become causally isolated because the repulsion will be pushing everything apart faster than the speed of light.

The different fits in Fig. 3 correspond to different matter – dark energy compositions. Without cosmological constant, the deviation is always negative but its rate of decrease depends on ΩM. The two lower curves show cases (ΩM = 0.35 and 1.00, respectively), which do not fit the measurements at all. Evidently, if the measurements are correct, some sort of dust or dark energy will be needed.

Because of the important consequences of these observations on cosmology, astronomers seriously investigate possible alternatives or data biases, such as possible effects of the evolution of SN Ia objects (deviation from the 'standard candle' behavior at low metallicity), effects of light absorption by the galaxy clusters hosting the supernovae, and by the intergalactic dust, lensing effects, etc. Although the actual dust content in the line of sight is not well determined, dust is not a problem in recent observations because astronomers make use of an empirical relation between the width of the SN Ia lightcurve (between rise and decay) and its absolute magnitude. By studying samples of closer SN Ia it was found that more energetic, brighter explosions also lead to a wider lightcurve. This is called the Phillips relation. It is not affected by dust absorption and the only assumption entering is that it is universally valid for all SN Ia. Thus, knowing the easily determinable lightcurve width, the absolute magnitude can be derived and the distance calculated by comparison to the observed relative magnitude of the explosion.

The best fit rather indicates the presence of dark energy. This conclusion was largely determined by the object with largest z observed to date. In 2001, a SN Ia with z = 1.6 was reported with larger apparent luminosity than expected in a matter dominated or in an empty Universe (Riess et al. 2001<>, see 3). It can be reconciled with the small z observations by assuming that it exploded in an epoch when the matter part of the energy density was still dominant and the rate of the expansion was decreasing. Quantitatively, the fit led to ΩM = 0.35, ΩΛ = 0.65.

The important question to be addressed in this context is the one regarding alternatives concerning the nature of the repulsive force. A cosmological constant implies an equation-of-state with w = -1 but any w < -1/3 yields repulsion. An additional, previously unknown, form of energy has been postulated as an alternative to the cosmological constant: Quintessence (Caldwell et al. 1998; Armendariz-Picon et al. 2000). It has repulsive properties but w ≠ -1. Therefore, it can be time-dependent and even have different values at different spatial points, contrary to a cosmological constant. Detailed SN Ia investigations try to put bounds not just on the size of the acceleration but also on the type of dark energy, i.e., the equation-of-state of the Universe.

The most recent analyses (Riess et al. 2007; Wood-Vasey et al. 2007) employing much larger data sets than before are all compatible with the cosmological constant (w = -1) interpretation of the data and give ΩM = 0.274 with 20% statistical error. A final conclusion concerning the acceleration driven by a substantial cosmological constant might be reached by the proposed Supernova Acceleration Probe space mission. The project aims at the observation of around 2,000 SN Ia up to a redshift z ≤ 1.2. Its launch is tentatively scheduled for 2013.

The results of 5 years of WMAP satellite mission were published and their cosmological interpretation was studied (Komatsu et al. 2009), taking into account the effect of the above-listed investigations. The results were interpreted by assuming that our Universe is flat and its energy content is a mixture of ordinary matter, gravitating dark matter, and dark energy. The most important cosmological parameters were determined with unprecedented accuracy. The accuracy was substantially increased by combining the WMAP CMBR data, type Ia supernova luminosity distance measurements, and the largest scale components of the 2dF galaxy cluster catalogue (Percival et al. 2007). The supernova data are sensitive to the energy density component of cosmological constant type, while the galaxy clusters represent the aggregates of the gravitating (mainly dark) matter. The analysis results in a value of the Hubble parameter H at present time of (70.1 ± 1.3) km s-1 Mpc-1. The ordinary matter content is (4.62 ± 0.15)%, the cold (nonrelativistic) dark matter represents (23.3 ± 1.3)%, the part of the dark energy in the full energy density is 72.1 ± 1.5%. The projection of the motion of such a Universe back in time leads to a highly accurate estimate of its age: 13.73 ± 0.12 billion years.

Concluding, it becomes a more and more established fact that the chemical elements formed from baryonic matter contribute less than 5% to the total energy density of the present Universe. In view of the complete symmetry of laws governing matter and antimatter in our present-day Universe it is actually a rather nontrivial fact that baryonic matter did not completely annihilate into radiation in the hot Universe directly after the inflationary epoch and also that the original energy density was transformed into a high-temperature gas of ordinary elementary particles.

2.2. Origin of the Matter–Antimatter Asymmetry

On the interface of neighboring domains of baryonic and antibaryonic matter, quark–antiquark (proton–antiproton) annihilation would lead to the emission of hard X-rays. The absence of this signal makes it highly probable that even if antibaryons were present in the early, hot Universe they had disappeared before the CMBR was emitted. Therefore, the observed baryonic density actually proves the presence of a matter–antimatter asymmetry within the present horizon in our Universe (Rubakov and Shaposhnikov 1996; Riotto and Trodden 1999).

In 1967, Sakharov analyzed the conditions that might lead to this asymmetry dynamically, instead of simply assuming it to be fixed by some initial conditions (Sakharov 1967). If, in a certain moment,

  1. The elementary interactions violate the symmetry under the combined transformation consisting of spatial reflection (P) followed by charge conjugation (C) – the so-called CP symmetry,

  2. The elementary interactions violate the baryon-antibaryon symmetry,

  3. The Universe is out of thermal equilibrium,

then a matter–antimatter density difference is produced. One can deduce the actual amount of asymmetry with detailed quantitative calculations.

Without going into details, some of the scenarios proposed by theoretical particle physicists for the creation process of this fundamental asymmetry will be outlined below. For this, a short account of the Standard Model of elementary interactions (Perkins 2000) is given first. (See also Chap. 10, Vol. 1)

Known elementary constituents of matter are quarks and leptons (see Table 1). Three families have been discovered. In each family one has two flavors of quarks and one lepton with the associated neutrino. The decay of the free neutron observed in 1932 and described first by the Fermi theory of weak interactions is understood today as the decay of a d-quark (one of three quarks composing the neutron) into a u-quark (which forms the final proton with the unchanged other two quarks) and an electron plus its antineutrino. The particles participating in this process constitute the lightest (first) particle family of the Standard Model.

Table 1. Elementary particles in the Standard Model. For each family, the first line in the center column refers to quark species of left- and right-handedness (L, R), the second line gives the same for the leptons, not participating in strong interaction processes. Those appearing in a bracket form a doublet with respect to SU(2)L transformations. The field quanta mediating strong, electromagnetic, and weak interactions are listed in the last column. They are not specific to any particle family

Particle families Matter constituents (each has its own anti-particle) Interaction vector particles

1st (uL, dL), uR, dR
(eL, veL), eR 8 gluons
2nd (cL, sL), cR, sR Photon (γ)
L, vμL), μR Weak quanta (Z0, W±)
3rd (tL, bL), tR, bR
L, vτL), τR

Three elementary interactions act among these particles. Each of them is mediated by vector particles. The electromagnetic quanta, the photons, bind nuclei and electrons into atoms and molecules. Weak interactions are mediated by three vector fields, the W± and the Z0, all discovered in 1983. Gluon fields bind the quarks into protons and neutrons. The strong interaction quanta come in eight different, so-called colored states and also each quark can appear in one of three different colored states.

It has been shown that the three Sakharov conditions might be fulfilled simultaneously in the Standard Model at high temperatures. The CP-violation, which allows the oscillation of the K0 and of the B0 mesons into their antiparticles and back, has been observed experimentally (in 1967 and 2001, respectively) and can be quantitatively understood with the present theory (Amsler et al. 2008).

On the other hand, no sign of baryon number violation has been observed to date in any elementary particle physics experiment. In the Standard Model, one cannot find any process that would involve the transformation of a proton into mesons or leptons. However, in the early 1970s, 't Hooft (1976) showed that in the presence of specific configurations of electro-weak vector fields, fermions (leptons and quarks) can be created or annihilated, but the difference of the baryon number and of lepton number (B - L) should stay constant (quarks and antiquarks actually carry ±1/3 unit of baryon charge, while the lepton charge of the known species is ±1). Today the chance for such transitions to occur is negligible (the probability is estimated to about 10-170). However, they must have occurred frequently when the temperature was of the order of 100 GeV (about 1015 K).

It is a very interesting coincidence that exactly at that temperature scale one expects the transformation of all elementary particles from massless quanta into the massive objects observed in today's experiments. The creation of the mass is due to the so-called Higgs effect. This consists of the condensation of an elementary scalar field (a close relativistic analogue of the Cooper-pairing in superconductivity). If this transformation had proceeded via a sufficiently strong first-order phase transition, the third of Sakharov's criteria had been also fulfilled by the behavior of the known elementary interactions in the very early Universe.

In a first-order phase transition, the low-temperature (massive) phase would appear via thermal nucleation, which is a truly far-from-equilibrium process. Inside the bubbles of the new phase the baryon number-violating processes are stopped. So the question is this: What is the net baryon concentration frozen?

Quarks and antiquarks traverse the phase boundaries, which represent a potential barrier for them. As a consequence of the complex CP-violating phase in the Hamiltonian describing weak interactions, the reflection and transmission amplitudes for matter and antimatter turn out to be different leading to an asymmetry in the constitution of matter and antimatter inside the bubbles.

The quantitative details of this beautiful scenario critically depend on a single parameter: the strength of the self-coupling of the so-called Higgs field, whose condensation determines the masses of all particles. This parameter is still unknown. The latest lower bound (Amsler et al. 2008) lies in a region where the phase transformation is actually continuous (beyond the end point of the first-order transition line). The situation could be different in supersymmetric extensions of the Standard Model. The one explored best is the electroweak phase transition within the so-called Minimal Supersymmetric Standard Model (Carena et al. 2009). One expects considerable guidance from measurements at the Large Hadron Collider in constraining the parameter space to search for the origin of baryon–antibaryon asymmetry. Another avenue could be the very late (low-energy density) exit from the inflationary period of evolution (Garcia-Bellido et al. 1999; Krauss and Trodden 1999; van Tent et al. 2004). If this energy scale coincides with the electroweak mass scale then the reheating of the Universe from its cold inflationary state would offer an out-of-equilibrium situation. This is the basis of the proposition of the cold baryogenesis scenario (Tranberg et al. 2007).

The resolution of the matter–antimatter asymmetry problem is an issue of central importance in particle physics in the twenty-first century.

2.3. Evolution of the Expanding Universe

The equilibrium in the hot particle "soup" is maintained through frequent elementary particle reactions mediated by the quanta of the three fundamental interactions. The expansion of the Universe dilutes the densities and, consequently, the reaction rates get gradually lower. The adiabatic expansion lowers monotonically also the temperature (the average energy density). (Actually, there is a one-to-one mapping between time and temperature.) The following milestones can be listed in the thermal history of the Universe (Kolb and Turner 1990).

First, the weak interaction quanta became massive at the temperature scale of 100 GeV. Since then, weak reactions have only occurred in contact interactions of the particles. At about the same time the t-quark and the Higgs quanta also decoupled from the 'soup'. The same decoupling happened for the other heavy quark species (b-quark, c-quark) and for the heaviest of the leptons (τ-particle) in the range 1–5 GeV (a few times 1013 K) of the average energy density. The τ-neutrinos remain in thermal equilibrium via weak neutral interactions.

The strong interaction quanta, the gluons became extremely short ranged at around the temperature kT ∼ 100–200 MeV (a few times 1012 K). Computer-aided quantum field theoretical investigations have demonstrated that quarks and gluons are confined to the interior of nucleons (protons and neutrons) and excited baryonic resonances below this temperature range (Petreczky 2007). This transformation was smooth for baryonic matter densities characteristic of our Universe at that epoch and for the actual mass values of the light quarks, very similar to the process of atomic recombination.

At this stage no nuclear composite objects can be formed yet, since they would instantly disintegrate in collisions with hard electromagnetic quanta. The stabilization occurs for temperatures below 0.1 MeV. Primordial synthesis of light nuclei took place at that cooling stage of the Universe (Sect. 3).

Below this temperature, light nuclei and electrons form a globally neutral plasma, in which thermal equilibrium is maintained exclusively by electromagnetic interactions. The gravitational attraction of the massive and electrically screened constituents of matter was balanced by the radiation pressure. This dynamical equilibrium is described by coupled fluid equations and results in acoustic oscillations modulating the essentially homogeneous distribution of the constituents (Hu 2001). The dominant wavelength of these oscillations is determined by those density fluctuation modes that left the horizon during inflation and are continuously reentering, since during the radiation-dominated period, the horizon expands faster than the global scale parameter of the Universe increases.

The last qualitative change occurred at the energy scale around 1 eV (∼104 K), when at the end of atomic recombinations the Universe became transparent to the propagation of electromagnetic radiation. At this moment the size of the Universe was about 1/1000 of its present radial scale. Today, the light emitted in the act of the last scattering is detected as cosmic microwave background radiation. A consistent interpretation of the details of its features represents (together with the primordial abundance of light nuclei) a unique test of all ideas concerning the earlier evolution of the Universe.

2.4. Gravitational Clustering of Matter

At the moment of the decoupling of light, the matter in the Universe became gravitationally unstable against density fluctuations. The key feature in understanding the emergence of a large-scale structure in the Universe is the statistical characterization of the density fluctuations at this moment. These fluctuations are determined by the spectra of the acoustic oscillations, which are in turn determined by the reentering density fluctuations of inflationary origin. This line of thought leads us to the hypothesis of the quantum origin of the largest-scale structures observed in the Universe.

Amplitudes of density fluctuations at different wavelengths follow independent Gaussian (also called normal) statistics (see Sect. 3.6, Chap. 9, Vol. 1), and their mean spectral power is distributed in an almost scale-invariant manner, described above. The absolute normalization was determined by the COBE satellite to be 1 part in 100,000. Their evolution can be analyzed initially with the help of the linearized gravitational equations. The classical analysis, originally performed by Jeans (1902), leads to the conclusion that fluctuations above the Jeans-scale are unstable and they are at the origin of the formation of the oldest structures (for a modern textbook on the subject, see Peacock 1999).

The nonlinear stage of the clustering process can only be followed by numerical integration of Newton's equations of motion for a very large number (typically 106–107) of equal-mass particles. The most interesting question studied in these N-body simulations concerns the mass distribution of the first galaxies. This feature determines the frequency of the occurrence of densities sufficiently high to start nuclear fusion reactions in these first gravitationally bound galactic objects.

The semiempirical theory (Press and Schechter 1974) assumes that this distribution is determined by the probability of matter fluctuations obeying a Gaussian distribution to exceed an empirically determined threshold value. This simple idea results in an ∼M-2/3 power scaling for the statistics of the collapsed objects with different mass M. This means that the earliest collapsed gas clouds were small, about 105 solar masses, and had a temperature of a few hundred Kelvin. The thermal excitation of H2 molecules provides the microscopic mechanism for the further radiative cooling, which might have led to the formation of the first minigalaxies and/or quasars. If sufficient quantities of H2 molecules were present, then the first stars and black holes were born very early, at a redshift z ∼ 20 i.e., some 12 billion years ago, when the characteristic size of the Universe was z + 1 times smaller than it is at present). If the dominant radiative cooling mechanism was the excitation of the atomic hydrogen, then the first objects with nearly 108 solar masses were formed at a temperature of 104 K. The first galaxies appeared in this case only for a redshift z ∼ 10. One expects that astronomical surveys of the coming years will be able to reach the distance that can be calculated from the Hubble law d = H/v, where the Hubble parameter H was defined in Sect. 2.1.4. The exploration of this distance scale should bring evidence for the existence of the first galaxies. According to the latest WMAP results (Komatsu et al. 2009) the first galaxies were formed at z = 10.8 ± 1.4.

The Millenium simulation (Springel et al. 2005) is an N-body simulation tracing over 10 billion mass points, representing fractions of the primordial gas, from the time of the CMBR decoupling to the present-day Universe. This simulation showed that it was necessary to assume cold dark matter (consisting of slowly moving, heavy particles) to reproduce the large-scale structures found in galactic surveys. It was also able to show that bright quasars are formed already at very early stages, thus confirming the observational results from the Sloane Digital Sky Survey (Anderson et al. 2001; Abazajian et al. 2009) that challenged traditional models of structure formation.

The radiative cooling and further gravitational evolution of the collapsed clouds lead to the appearance of the first stars (see Sect. 4.1.1).

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