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Introduction to particle cosmology. The standard model of cosmology and its open problems. (English) Zbl 1334.85001

Unitext for Physics. Berlin: Springer (ISBN 978-3-662-48077-9/hbk; 978-3-662-48078-6/ebook). xi, 251 p. (2016).
Cosmology, the importance of which is more and more increasing in physics, is the science of the dynamics of the Universe on large scales. Nowadays, using modern advanced instruments, it is possible to measure cosmological parameters with very high precision, and therefore to use the Universe as a laboratory to test elementary particle physics. The obervations show that “there is an unambiguous astronomical evidence strongly requiring new physics beyond the Minimal Standard Model (MSM) of particle physics and maybe beyond General Relativity.” (ibid.page 1).
This book describes the so-called Standard Cosmological Model. The model’s theoretical aspects are based on General Relativity and on the Standard Model of particle physics, with the addition of the inflationary paradigm. This scenario is very successful in explaining a large amount of observational data including, in particular, the description of the Universe expansion, the primordial abundances of the light elements, as well as the origin and properties of the cosmic microwave background radiation. However, there exist observed phenomena that do not fit to the Standard Model of particle physics and cosmology, e.g.the matter-antimatter asymmetry, the accelerated expansion of the contemporary Universe, and the dark matter.
The present book consists of 12 chapters. Chapter 1 of the textbook briefly reviews the milestones of modern cosmology. Then, these milestones are discussed in the rest of the book in more detail. Again and again problems are pointed out, which are not solved within the frame of the present Standard Model of Cosmology.
Chapter 1 starts with the problems of Newtonian cosmology. After that, the Standard Model of cosmology is explained. The so-called big bang model of the Universe is introduced. According to this model, the Universe started expanding from an infinitely dense primordial plasma. The big bang has, however, to be interpreted with caution because the Friedmann equations which are used there predict a spacetime singularity and an infinite energy density of matter, which are most likely pathologies of classical General Relativity. After the big bang, the temperature and the particle density of the Universe dropped down. As a consequence, the particle reaction rates decreased with time. Some particles stopped their interaction with the rest of the plasma, so that relics were produced, which, if they are stable, may yet exist today.
But the physics above 200 GeV is not yet known. Consequently the predictions of the main events in the history of the Universe from the big bang singularity to the present day depend on specifically assumed physical models. Moreover, for the time being, there do not exist observations before the big bang nucleosynthesis (1-15 min after big bang, temperature 1-0.05 MeV). Thus, although the electroweak (\(10^{-11}\) s after big bang, temperature 200 MeV) and the quantum chromodynamic (\(10^{-5}\) s after big bang, temperature 200 MeV) phase transitions can be expected from the known physics, there is no proof that the Universe had at the assumed times the suggested temperatures. For instance, the production of deuterium did not start when the temperature of the Universe equalled the deuterium binding energy of about 2 MeV. It began later, as the number of photons was still large enough to destroy deuterium before the temperature cooled down to 80 keV. The same is valid for the formation of the cosmic microwave background (CMB) which occurred at about 0.3 eV. Although hydrogen has a binding energy of 13.6 eV, the Thomson scattering of photons by the free electrons was yet too strong at such a temperature, and decreased the electron-proton recombination rate. Only at temperatures less than 0.3 eV, the photons, forming now the CMB, decoupled from the matter.
The detection of CMB anisotropies of the order of \(10^{-5}\) by the COBE satellite is considered as the birth of cosmology as precise science. At the same time it was suggested that this fact results into the conclusion that different parts of the sky were causally connected at the time of the last photon scattering, which is not in agreement with the Friedmann model (horizon problem).
A way to solve the problems of dangerous relics, of flatness and horizon of the Universe - and also of primordial inhomogeneities at cosmological scales as seeds of galaxies - was to postulate a period of exponential cosmological expansion of the Universe, the so-called inflation. But, at present, the inflatory hypothesis is still at the level of speculation.
Further, today there are several scenarios, that can potentially explain the matter-antimatter asymmetry of the Universe. However, they typically involve physics at too high energies to be tested with recent particle colliders. Concerning the dark matter problem it is explained, that the neutrinos of the Standard Model would have the correct interaction properties, but their mass is too low to contribute a significant fraction of the cosmological dark matter. Good dark matter candidates exist in theories beyond the MSM. However, so far, no observational evidence exists. Further, the problem of the non-constant cosmological “constant” is discussed. It is concluded, that it may be solved by both the introduction of a perfect fluid with unusual equation of state (a pressure proportional to minus particle mass density) or a General Relativity beyond the classical Einstein’s one.
A simple estimate of the age of the Universe, considering a constant expansion rate, gives 14 Gyr. A more accurate estimate requires the knowledge of the energy content of the Universe. Therefore today, one acts on the assumption, that the age is about 13.8 Gyr, which is consistent with the age of the oldest stars in globular clusters, which are supposed to have formed 1-2 Gyr after the big bang. At present, we also do not know the actual size of the whole Universe. If the Universe has a finite size, it must be anyway larger than the visible Universe.
Chapter 1 ends with cosmological models beyond General Relativity. All these models are up to now speculations. In many extensions of the theory, the gravity may become repulsive at a critical, large mass density. Instead of the big bang, a bounce occurs moving the origin of the Universe to an earlier time. A further extension of such models concludes that our Universe was born from the gravitational collapse of a region in another universe.
Chapter 2 provides a short review on General Relativity, focusing on the concepts necessary for an introductory course on cosmology. It is shown that the gravitational force can be interpreted as deformation of the geometry of the spacetime, which is not flat anymore. The motion of the particles is determined by the geodesic equations. And how the spacetime is curved by the energy is described by the Einstein’s equations. The last equations are second-order non-linear partial differential equations for the metric coefficients, which are difficult to solve.
Chapter 3 deals with the Standard Model of particle physics, which currently represents the best framework for the description of all known elementary particles and all fundamental forces of Nature except gravity. Within the frame of the model, matter is described by fermions with spin-1/2, which are grouped into two classes, leptons and quarks. Forces are described by gauge theories and are mediated by gauge bosons, spin-1 particles. The Standard Model also includes a spin-0 particle, the Higgs boson, which provides a mass to the other fundamental particles (charged leptons, quarks, week gauge bosons). Particles are classified according to their quantum numbers, which are related to the invariance of the theory under certain symmetries. Chapter 3 underlines that according to the Standard Model neutrinos are massless, what is not correct. The chapter ends with discussions beyond the MSM, such as the stability of the Higgs boson and the phenomenon of neutrino oscillations. The MSM allows the existence of a CP (charge-parity) violating term in quantum chromodynamics (QCD), but up to now no way was found to arrange inflation. Finally, in the chapter, a recipe is provided to get a rough estimate of cross sections of scattering processes on the basis of leading order Feynman diagrams.
Various cosmological models are explained in chapter 4. The simplest model bases on the Friedmann-Robertson-Walker metric taking the cosmological principle into account, according to which the Universe is homogeneous and isotropic. Solving Einstein’s equation, one then obtains the already discussed Friedmann cosmology. The dynamics of the Universe may depend on the domination of matter, radiation or vacuum. Current observations support the so-called \(\Lambda\) cold dark matter model (\(\Lambda\)CDM model), in which the Universe is almost flat, and today it is dominated by a vacuum-like energy.
Chapter 5 studies the kinetics and thermodynamics in cosmology. In cosmology, reactions between particles are faster if the Universe is younger, and less time is necessary to reach thermal equilibrium. In thermal equilibrium, the state of matter may be described by a few parameters, e.g.the temperatures and the chemical potentials of the particles. The distribution of the particles over their energy is determined by the equilibrium and it is given by the canonical Fermi-Dirac or Bose-Einstein forms. Theoretical descriptions of the Universe are simplified taking an equilibrium state into account, but the interesting phenomena in the Universe such as freezing of massive particles, distortion of the massless neutrino spectrum and baryogenesis, appear far from an equilibrium state.
Chapters 6 and 7, dealing, respectively, with inflation and baryogenesis, are more advanced and require some knowledge of quantum field theory. Chapter 6 starts with the explanation of mechanisms that could lead to an exponential cosmological expansion. It is shown that an important condition for the (quasi-)exponential expansion is a (quasi-)constant Hubble parameter. Of course, at constant Hubble parameter, the vacuum energy does not change with the time and the exponential expansion would exist forever. In realistic inflationary models, the expansion could be governed by a scalar field \(\phi\) called inflaton, with an only approximately constant energy density. In the course of the cosmological expansion, the energy of the inflaton field drops down, first very slowly when \(\phi\approx\mathrm{const}\). Later, when \(\phi\) begins to oscillate, the stored vacuum-like energy of \(\phi\) turns into the energy of a hot “soup” of elementary particles. At the first stage, the Universe looks like a dark expanding empty place. The second stage is then a big bang, where the primeval plasma is created. “It is impressive that the total mass/energy of matter inside the observed Universe volume is by far larger than the initial mass/energy inside the microscopic volume from which the Universe originated. Still it agrees with the energy conservation law.” (p.95). It is pointed out that within an exponentially expanding non-singular cosmology by S. Gottlöber et al. [Int. J. Mod. Phys. D 1, No. 2, 257–279 (1992; Zbl 0935.83520)], during the initial exponential stage, gravitational waves are produced, which may yet be observable at the present time. “If observed, it would be one of the strongest “experimental” evidence for the existence of a primordial inflation” (p.94). [11.February 2016, the detection of gravitational waves was announced by the LIGO research team].
Further, a canonical scalar inflaton, i.e.a hypothetical scalar field that is supposed to be responsible for cosmic inflation, with power law potential, is considered. Pointed out are also other mechanisms of inflation, so e.g.the double field or hybrid inflation. Perturbative, non-perturbative and parametric-resonance heating of the Universe are discussed in chapter 6. The production of particles by an inflaton field and by simultaneous action of a gravitational field are discussed, but also the generation of gravitational waves at the end of inflation as well as the generation of primordial density perturbations by inflation.
Noted is also a double-field or hybrid inflation. An example is explained where the inflation is coupled to a lighter, homogeneous field through a trilinear coupling (perturbative production). Also a rigorous theory of particle production by an external field based on the Bogolyubov transformation is presented (non-perturbative phenomena).
Chapter 7 deals with the baryogenesis of the Universe. It is noted that tha total amount of baryonic matter can be determined from big bang nucleosynthesis (BBN) and CBM data under the assumption of a negligible amount of antimatter. The agreement between the two different methods, basing on data when the Universe was 100 s (BBN) and 370000 yrs (CBM), is a very strong argument in favor of the correctness of the general cosmological picture.
Chapter 7 discusses general features of baryogenesis models as the Sakharov principles (non-conservation of baryonic number, breaking of C and CP invariance, deviation from thermal equilibrium). It is shown that none of the principles is obligatory, but baryogenesis models without them require some exotic mechanisms. Further, a scenario is briefly described, which allows for abundant antimatter even in a galaxy. On the other hand, recent discoveries are discussed which are at odds with the Standard Model. There were observed stars in the galaxy, which have an unexpectedly high age. Further, supermassive black holes were observed, which cannot have formed in accordance with the standard scenario of formation of central galactic, supermassive black holes by accretion of matter in the central part of a galaxy. The black holes must have formed first, and then they attracted matter serving as seeds for a galaxy formation.
The big bang nucleosynthesis is described in chapter 8 as production of light elements in the early Universe, a few minutes after the big bang, when the temperature of the plasma was 1 MeV - 10 keV. The calculation of the abundances of light elements is governed by the Friedmann equations, the matter content of the Standard Model of particle physics, the properties of elementary particles, especially those of neutrinos, and nuclear reaction rates that can be measured in laboratory. The freeze-out of the weak interaction at a temperature of the Universe of 1 MeV and the deuterium bottleneck at about 70 keV are discussed. Abundances of the light elements are shown to be a function of the baryon to photon number ratio \(\eta\). Today, \(\eta\) may also be found from the study of the CBM anisotropy. It is concluded that most of the matter in the contemporary Universe may be made of weakly interacting massive particles beyond the MSM of particle physics.
Chapter 9 gives a review on dark matter. It starts with its observational evidence. Then it presents dark matter candidates, e.g.lightest supersymmetric particles like the neutralino, axions solving the strong CP-problem in QCD, but also super-heavy particles and primordial black holes. The chapter finishes with overviews on direct and indirect experimental searches for dark matter particles.
Chapter 10 discusses the Cosmic Microwave Background as a milestone in the establishment of the Standard Model of Cosmology. During the last 20 years, the CBM physics was strongly developed. Now, most of the cosmological parameters may be measured with a precision at the percent level. The physics of recent CBM physics is quite complicated technically. For this reason, the authors provide only a simple overview without many details. They consider the recombination of electrons and protons, and the decoupling of the photons from the matter. Then they explain in detail the formalism for the description of CMB fluctuations and analyze primary and secondary temperature anisotropies, produced at or before the last photon scattering and after it, respectively. Finally, also polarization anisotropies are discussed.
Chapter 11 deals with one of the most impressive discoveries in astronomy, made during approximately the last two decades, the acceleration of the expansion of the Universe. This was not expected for the motion of matter in a self-gravity field. The increase of the expansion speed started at a relatively recent cosmological epoch, at a redshift of order unity. Two acceleration mechanisms are explained, the so-called dark energy (or vacuum energy, cosmological constant \(\Lambda\)) corresponding to negative pressure, and a quasi-constant scalar field \(\phi\) analogous to that responsible for inflation. In the first case, the expansion will last forever for any three-dimensional geometry. In case of a light field \(\phi\) or a field with very flat potential, in a distant future, the expansion will be again decelerated. Further, it is also mentioned that an accelerated expansion could be induced if the gravitational interaction is modified at small curvature.
Density perturbations and the behavior of instabilities of self-gravitating systems are discussed in chapter 12. The chapter starts with density perturbations in a non-relativistic Newtonian gravity field. Then, scalar perturbations in General Relativity are studied. The rise of density perturbations in a spherically symmetric and asymptotically flat background are analysed, which may depend on both time and space coordinates. Finally, the density evolution in the cosmological Friedmann-Robertson-Walker background is studied. The chapter ends with density perturbations at modified gravitational interaction.
The present book is intended for senior undergraduate and graduate physics students interested in cosmology. It is not necessary that they possess a strong background in theoretical high energy physics.

MSC:

85-02 Research exposition (monographs, survey articles) pertaining to astronomy and astrophysics
85A40 Astrophysical cosmology
83F05 Relativistic cosmology
81V25 Other elementary particle theory in quantum theory
83C55 Macroscopic interaction of the gravitational field with matter (hydrodynamics, etc.)
83D05 Relativistic gravitational theories other than Einstein’s, including asymmetric field theories
85A25 Radiative transfer in astronomy and astrophysics
83C35 Gravitational waves
81V05 Strong interaction, including quantum chromodynamics
81T20 Quantum field theory on curved space or space-time backgrounds
83C40 Gravitational energy and conservation laws; groups of motions
83C75 Space-time singularities, cosmic censorship, etc.
83C57 Black holes
53Z05 Applications of differential geometry to physics
83C10 Equations of motion in general relativity and gravitational theory
80A10 Classical and relativistic thermodynamics

Citations:

Zbl 0935.83520
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