Introduction to the Theory of the Early Universe

The following sections are included:

• Dedication
• Preface to the 2nd Edition
• Preface to the 1st Edition
• Contents

The purpose of this Chapter is to give a preview of the field which we consider in this and the accompanying book. The presentation here is at the qualitative level, and is by no means complete. Our purpose is to show the place of one or another topic within the entire area of cosmology.

In this book we use the basic notations and equations of General Relativity; see Appendix A. The notations and conventions are summarized in Sec. A.11.

The following sections are included:

• Friedmann Equation
• Sample Cosmological Solutions. Age of the Universe. Cosmological Horizon
  • Non-relativistic matter (“dust”)
  • Relativistic matter (“radiation”)
  • Vacuum
  • General barotropic equation of state p = wρ
• Solutions with Recollapse

The following sections are included:

• Composition of the Present Universe
• General Properties of Cosmological Evolution
• Transition from Deceleration to Acceleration
• Transition from Radiation Domination to Matter Domination
• Present Age of the Universe and Horizon Size
• Brightness–Redshift Relation for Distant Standard Candles
• Angular Sizes of Distant Objects
• *Quintessence
  • Evolution of scalar field in expanding Universe
  • Accelerated cosmological expansion due to scalar field
  • Tracker field

The following sections are included:

• Distribution Functions for Bosons and Fermions
• Entropy in Expanding Universe. Baryon-to-Photon Ratio
• *Models with Intermediate Matter Dominated Stage: Entropy Generation
• *Inequilibrium Processes

The following sections are included:

• Recombination Temperature in Equilibrium Approximation
• Photon Last Scattering in Real Universe
• *Kinetic Equilibrium
  • Energy transfer from photons to electrons
  • Coulomb scattering: thermal equilibrium of electron-proton component
  • Thermal (in)equilibrium of photons
• Horizon at Recombination and its Present Angular Size. Spatial Flatness of the Universe

The earlier the period in the history of the Universe, the higher the temperature and density of matter. Hence, those processes which are too weak to be relevant in the present Universe, are important at earlier stages and may leave imprints in the Universe we see today.

The earliest epoch in the hot Universe which has been tested observationally is the Big Bang Nucleosynthesis epoch (BBN). As we will see, it begins at temperature of about 1MeV and lasts until the temperature drops to a few dozen keV. At this time, neutrons in cosmic medium combine with protons into light nuclei, mostly helium-4 (⁴He = α-particle) with small but measurable admixture of deuterium (D≡²H), helium-3 (³He) and lithium-7 (⁷Li). The main thermonuclear reactions of BBN are listed in the beginning of Sec. 8.3. We will see that at relevant temperatures neutrons are less abundant than protons; “extra” protons remain free and in the end form hydrogen atoms.

As we have discussed already, large contribution to the total energy density in the present Universe (about 25%) comes from dark matter which consists, most likely, of new massive particles absent in the Standard Model of particle physics. These particles must be non-relativistic and should have practically no interactions with photons. The latter requirement comes from the observations showing that dark matter halos are much larger than baryon parts of galaxies, meaning that dark matter experiences very little, if any, photon cooling (see Fig. 1.7 in Chapter 1).

As we mentioned in Chapter 1, there are no direct experimental indications yet that temperatures above a few MeV existed in the Universe. Nevertheless, it is natural to assume that the Universe in the past had much higher temperatures. Properties of cosmic medium were very different at different temperatures. In particular, there could occur phase transitions associated with the rearrangement of the ground state.

As we discussed in Secs. 1.3 and 5.2, there are baryons and no antibaryons in the present Universe. The present baryon abundance is characterized by the baryonto-photon ratio η_B = n_B,0/nγ,0 ≃ 6.05 · 10⁻¹⁰. Another way to quantify the baryon asymmetry is to use the baryon-to-entropy ratio (see Sec. 5.2)

In this Chapter we consider cosmological aspects of field theory models which admit soliton or soliton-like solutions. These solutions are specific (sometimes macroscopic) field configurations whose stability is ensured either by non-trivial topology of the space of vacua (topological defects) or by the existence of conserved global quantum numbers (non-topological solitons, Q-balls). Of interest are both particle-like solitons (monopoles, Q-balls) and extended objects (cosmic strings, domain walls); we will jointly call them defects or solitons in what follows. These objects are absent in the Standard Model (modulo exotic proposals like quark nuggets), but they naturally exist in some extensions of the Standard Model. Generally speaking, there may be also unstable solutions whose lifetime is comparable to the Hubble time.

The following sections are included:

• Appendix A Elements of General Relativity
  • Tensors in Curved Space–Time
  • Covariant Derivative
  • Riemann Tensor
  • Gravitational Field Equations
  • Conformally Related Metrics
  • Interaction of Matter with Gravitational Field. Energy–Momentum Tensor
  • Particle Motion in Gravitational Field
  • Newtonian Limit in General Relativity
  • Linearized Einstein Equations about Minkowski Background
  • Macroscopic Energy–Momentum Tensor
  • Notations and Conventions
• Appendix B Standard Model of Particle Physics
  • Field Content and Lagrangian
  • Global Symmetries
  • C-, P-, T-Transformations
  • Quark Mixing
  • Effective Fermi Theory
  • Peculiarities of Strong Interactions
  • The Effective Number of Degrees of Freedom in the Standard Model
• Appendix C Neutrino Oscillations
  • Oscillations and Mixing
    • Vacuum oscillations
    • Three-neutrino oscillations in special cases
    • Mikheev–Smirnov–Wolfenstein effect
  • Experimental Discoveries
    • Solar neutrinos and KamLAND
    • Atmospheric neutrinos, K2K and MINOS
    • Accelerator and reactor neutrinos:|U_e3|
  • Oscillation Parameters
  • Dirac and Majorana Masses. Sterile Neutrinos
  • Search for Neutrino Masses
• Appendix D Quantum Field Theory at Finite Temperature
  • Bosonic Fields: Euclidean Time and Periodic Boundary Conditions
  • Fermionic Fields: Antiperiodic Boundary Conditions
  • Perturbation Theory
  • One-Loop Effective Potential
  • Debye Screening

The following sections are included:

• Bibliography
• Books and Reviews
• Index