Introduction to the Theory of the Early Universe

Hot Big Bang Theory

Dmitry S Gorbunov, Valery A Rubakov

• Publisher: WSPC
• Year: 2011
• Print ISBN: 9789814343978
• eBook ISBN: 9789814390620
• Topic: Physical Sciences
• Subtopic: Astronomy & Astrophysics

This book is written from the viewpoint of a deep connection between cosmology and particle physics. It presents the results and ideas on both the homogeneous and isotropic Universe at the hot stage of its evolution and in later stages. The main chapters describe in a systematic and pedagogical way established facts and concepts on the early and the present Universe. The comprehensive treatment, hence, serves as a modern introduction to this rapidly developing field of science. To help in reading the chapters without having to constantly consult other texts, essential materials from General Relativity and the theory of elementary particles are collected in the appendices. Various hypotheses dealing with unsolved problems of cosmology, and often alternative to each other, are discussed at a more advanced level. These concern dark matter, dark energy, matter-antimatter asymmetry, etc.

This book is accompanied by another book by the same authors, Introduction to the Theory of the Early Universe: Cosmological Perturbations and Inflationary Theory and is available as a set.

Sample Chapter(s)
Chapter 1: Cosmology: A Preview (1,644 KB)
Chapter 11: Generation of Baryon Asymmetry (701 KB)

Contents:

• Cosmology: A Preview
• Homogeneous Isotropic Universe
• Dynamics of Cosmological Expansion
• ΛCDM: Cosmological Model with Dark Matter and Dark Energy
• Thermodynamics in Expanding Universe
• Recombination
• Relic Neutrinos
• Big Bang Nucleosynthesis
• Dark Matter
• Phase Transitions in the Early Universe
• Generation of Baryon Asymmetry
• Topological Defects and Solitons in the Universe
• Color Pages

Readership: Cosmologists, advanced undergraduate and graduate students.

Chapter 1

Cosmology: A Preview

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.

Before proceeding, let us introduce units and conventions that we use throughout this book.

1.1 Units

We mostly use the “natural” system of units in which the Planck constant, speed of light and the Boltzmann constant are equal to 1,

Then the mass M, energy E and temperature T have the same dimension (since [E] = [mc²], [E] = [k_BT]). A convenient unit of mass and energy is 1 eV or 1 GeV = 10⁹ eV; the proton mass is then equal to m_p = 0.938 GeV, and 1 K is approximately 10⁻¹³ GeV. Time t and length l in the natural system have dimension M⁻¹ (since [E] = [ħω], [ω] = [t⁻¹] and [l] = [ct]), with 1 GeV⁻¹ ~ 10⁻¹⁴ cm and 1 GeV⁻¹ ~ 10⁻²⁴ s. We give the coefficients relating various units in Tables 1.1 and 1.2.

Problem 1.1. Check the relations given in Tables 1.1 and 1.2. What are 1 Volt (V), 1 Gauss (G), 1 Hertz (Hz) and 1 Angström (Å) in natural system of units?

In natural system of units, the Newton gravity constant G has dimension M⁻². This follows from the formula for the gravitational potential energy

since [V] = M, [r⁻¹] = M. It is convenient to introduce the Planck mass M_Pl in the following way,

Numerically

Table 1.1 Conversion of natural units into CGS units.

Energy	1 GeV = 1.6 · 10^−3 erg
Mass	1 GeV = 1.8 · 10^−24 g
Temperature	1 GeV = 1.2 · 10^13 K
Length	1 GeV^−1 = 2.0 · 10^−14 cm
Time	1 GeV^−1 = 6.6 · 10^−25 s
Particle number density	1 GeV^3 = 1.3 · 10^41 cm^−3
Energy density	1 GeV^4 = 2.1 · 10^38 erg · cm^−3
Mass density	1 GeV^4 = 2.3 · 10^17 g · cm^−3

Table 1.2 Conversion of CGS units into natural units.

Energy	1 erg = 6.2 · 10^2 GeV
Mass	1g = 5.6 · 10^23 GeV
Temperature	1 K = 8.6 · 10^−14 GeV
Length	1 cm = 5.1 · 10^13 GeV^−1
Time	1 s = 1.5 · 10^24 GeV^−1
Particle number density	1 cm^−3 = 7.7 · 10^−42 GeV^3
Energy density	1 erg · cm^−3 = 4.8 · 10^−39 GeV^4
Mass density	1 g · cm^−3 = 4.3 · 10^−18 GeV^4

and the Planck length, time and mass are

The gravitational interactions are weak precisely because M_Pl is large.

Problem 1.2. Check the relations (1.1) and (1.2).

Problem 1.3. What is the ratio of gravitational interaction energy to Coulomb energy for two protons?

The traditional unit of length in cosmology is Megaparsec,

1 Mpc = 3.1 · 10²⁴ cm.

Let us also introduce a convention which we use in this book. The subscript 0 denotes present values of quantities which can depend on time. As an example, ρ(t) denotes the energy density in the Universe as a function of time, while ρ₀ ≡ ρ(t₀) is always its present value.

There are several units of length that are used in astronomy, depending on sizes of objects and length scales considered. Besides the metric system, in use are

astronomical unit (a.u.), which is the average distance from the Earth to the Sun,

1 a.u. = 1.5 · 10¹³ cm;

light year, the distance that a photon travels in one year,

parsec (pc) — distance from which an object of size 1 a.u. is seen at angle 1 arc second,

1pc = 2.1 · 10⁵ a.u. = 3.3 light year = 3.1 · 10¹⁸ cm.

To illustrate the hierarchy of spatial scales in the Universe, let us give the distances to various objects expressed in the above units.

10 a.u. is the average distance to Saturn, 30 a.u. is the same for Pluto, 100 a.u. is the estimate of maximum distance which can be reached by solar wind (particles emitted by the Sun). 100 a.u. is also the estimate of the maximum distance to cosmic probes (Pioneer 10, Voyager 1, Voyager 2). Further out is the Oort cloud, the source of the most distant comets, which is at the distance of 10⁴ − 10⁵ a.u. ~ 0.1 − 1pc.

The nearest stars — Proxima and Alpha Centauri — are at 1.3 pc from the Sun. The distance to Arcturus and Capella is more than 10 pc, the distances to Canopus and Betelgeuse are about 100 pc and 200 pc, respectively; Crab Nebula — the remnant of supernova seen by naked eye — is 2 kpc away from us.

The next point on the scale of distances is 8 kpc. This is the distance from the Sun to the center of our Galaxy. Our Galaxy is of spiral type, the diameter of its disc is about 30 kpc and the thickness of the disc is about 250 pc. The distance to the nearest dwarf galaxies, satellites of our Galaxy, is about 30 kpc. Fifteen of these satellites are known; the largest of them — Large and Small Magellanic Clouds — are 50 kpc away. Search for new, dimmer satellite dwarfs is underway; we note in this regard that only eight of Milky Way satellites were known by 1994.

The mass density of the usual matter in usual (not dwarf) galaxies is about 10⁵ higher than the average over the Universe.

The nearest usual galaxy — the spiral galaxy M31 in Andromeda constellation — is 800 kpc away from the Milky Way. Despite the large distance, it occupies a sizeable area on the celestial sphere: its angular size is larger than that of the Moon! Another nearby galaxy is in Triangulum constellation. Our Galaxy together with Andromeda and Triangulum galaxies, their satellites and other 35 smaller galaxies constitute the Local Group, the gravitationally bound object consisting of about 50 galaxies.

The next scale in this ladder is the size of clusters of galaxies, which is 1–3 Mpc. Rich clusters contain thousands of galaxies. The mass density in clusters exceeds the average density over the Universe by a factor of a hundred and even sometimes a thousand. The distance to the center of the nearest cluster, which is in the Virgo constellation, is about 15 Mpc. Its angular size is about 5 degrees. Clusters of galaxies are the largest gravitationally bound systems in the Universe.

1.2 The Universe Today

We begin our preview with the brief discussion of the properties of the present Universe (more precisely, of its observable part).

1.2.1 Homogeneity and isotropy

The Universe is homogeneous and isotropic at large spatial scales. The sizes of the largest structures in the Universe — superclusters of galaxies and gigantic voids — reach¹ tens of Megaparsec. At larger scales all parts of the Universe look the same (homogeneity). Likewise, there are no special directions in the Universe (isotropy). These facts are well established by deep galaxy surveys which collected data from millions of galaxies.

About 20 superclusters are known by now. The Local Group belongs to a supercluster with the center in the direction of Virgo constellation. The size of this supercluster is about 30 Mpc, and besides the Virgo cluster and Local Group it contains about a hundred groups and clusters of galaxies. Superclusters are rather loose: the density of galaxies in them is only twice higher than the average in the Universe. The nearest to Virgo is the supercluster in Hydra and Centaurus constellations; its distance to Virgo supercluster is about half a hundred Megaparsec.

The largest catalog of galaxies and quasars up to date is the freely available catalog of SDSS [2] (Sloan Digital Sky Survey). This catalog is the result of the analysis of the data collected during almost 8 years of operation of a dedicated telescope, 2.5 meters in diameter, which is cap...

Table of contents

• Cover
• Half title
• Title
• Copyright
• Dedication
• Contents
• Preface
• 1. Cosmology: A Preview
• 2. Homogeneous Isotropic Universe
• 3. Dynamics of Cosmological Expansion
• 4. ΛCDM: Cosmological Model with Dark Matter and Dark Energy
• 5. Thermodynamics in Expanding Universe
• 6. Recombination
• 7. Relic Neutrinos
• 8. Big Bang Nucleosynthesis
• 9. Dark Matter
• 10. Phase Transitions in the Early Universe
• 11. Generation of Baryon Asymmetry
• 12. Topological Defects and Solitons in the Universe
• 13. Color Pages
• Appendix A Elements of General Relativity
• Appendix B Standard Model of Particle Physics
• Appendix C Neutrino Oscillations
• Appendix D Quantum Field Theory at Finite Temperature
• Books and Reviews
• Bibliography
• Index