Cosmology: Foundations and Frontiers

Description

Preface
1 Fundamental discoveries in cosmology
1.1. World of galaxies
1.2. Cosmological expansion
1.3. Cosmic Microwave Background
1.4. Dark matter
1.5. Dark energy
2 General Relativity and cosmology
2.1. Spacetime
2.2. Principle of Equivalence
2.3. The Schwarzschild metric
2.4. Orbits
2.5. Deflection of light
2.6. Black Holes
2.7. Rotating Bodies
2.8. Rotating Black Holes
2.9. Curvature of 3-space
2.10. Expanding Universe
2.11. The scale factor
2.12. Newtonian cosmology
2.13. The early Universe
2.14. Gravitational waves
3 Standard cosmological model
3.1. The observed Universe
3.2. Cosmic microwave background radiation
3.3. Baryonic matter
3.4. Dark matter
3.5. Cosmic vacuum
3.6. Physics of vacuum
3.7. Cosmic energy composition
3.8. Three epochs of cosmic evolution
3.9. Big Bang Nucleosynthesis
3.10. Cosmic plasma and radiation
4 Gravitational instability
4.1. Newton’s idea
4.2. Hydrodynamics
4.3. Jeans Criterion
4.4. Jeans length for collisionless gas
4.5. Jeans mass in the expanding Universe
4.6. Dynamics of gravitational instability
4.7. The mass contained in early structures
4.8. Perturbations of the gravitational potential
4.9. Rotational perturbations
4.10. Gravitational waves: tensor perturbations
4.11. Radiation damping
4.12. Radiation friction
4.13. Plasma diffusion
4.14. Free streaming in dark matter
4.15. Dark matter perturbations at radiation domination
4.16. Dark matter drag
4.17. Isothermal perturbations after recombination
4.18. Termination of gravitational instability
5 Formation of large scale structure
5.1. Harrison–Zeldovich spectrum
5.2. Evolution of the spectrum at lower scales
5.3. Power Spectrum
5.4. Galaxy groups and the vacuum dominated Hubble flow
5.5. Perturbations and cosmic microwave background
5.6. Observing CMB anisotropy
5.7. Correlations
5.8. The Virial Theorem
5.9. Cosmic Energy Equation
5.10. Nonlinear perturbations: spherical solution
5.11. Tolman solution
5.12. Nonlinear perturbations: plane solution
5.13. Zeldovich flow in vacuum background
5.14. Distributions of Halos
5.15. Baryons in Galaxies
5.16. Numerical Simulations
6 Evidence for dark matter
6.1. The Milky Way and other disk galaxies
6.2. The Local Group of Galaxies
6.3. Relaxation Time
6.4. Dynamical Friction
6.5. Equilibrium distributions of stellar systems
6.6. Weighing the clusters
6.7. Sunyaev–Zeldovich Effect
6.8. Subclusters
6.9. Gravitational Lensing
7 Evolution of galaxies
7.1. Quasars
7.2. Binary Black Holes
7.3. The General Three-Body Problem
7.4. Three Black Holes
7.5. Intergalactic Black Holes
7.6. The Population of Escapers
7.7. Forming stellar systems
7.8. The Lyman alpha Forest
8 Current results, problems and ideas
8.1. Is the Universe finite?
8.2. Cosmic internal symmetry
8.3. Gravity-electroweak interplay
8.4. Cosmic coincidences
8.5. Why does space look flat?
8.6. Cosmic entropy
8.7. The gross figures
8.8. Extra dimensions
8.9. What is natural?
8.10. Why does the Universe expand?
8.11. Why is the Universe uniform?
References
Index
Preface
Cosmology has seen phenomenally rapid developments in the last few years. These developments have created a need for textbooks which include fully the latest observations and theory. We want to give students the foundations, both analytic and observational, for modern cosmology. We describe how what were once new ideas became part of the solid present-day foundations, facts or concepts likely to endure. On the other hand, from this experience, we know that frontier observations or concepts currently on the edge of verification and acceptance may well extend our future understanding of the universe as has happened recently.

Our approach is on the conservative side, and thus we do not spend much time with topics like the inflation theory where fashions are likely to change many times even before this book comes out of print. Thus this text is not meant as a course in Astro-Particle Cosmology, even though we treat some current ideas of this field also. A good introduction to cosmology with particle physics emphasis is given in the book by Matts Roos Introduction to cosmology (Wiley, 2003). It is our experience, that the best students should not only be presented with well-established ideas, but also should see more speculative frontier material to excite their interest and active thought. A bit of this is found also in this text, mostly in the last chapter.

Beside the main text, we often present boxes, containing either a digression into an interesting side area or background material. Scattered through the text, at appropriate locations are problems or exercises to enable better understanding.

The present text grew out of lecture notes for the courses on Physical Cosmology, Galactic Evolution and Galactic Dynamics which the authors have given over the years in University of Turku and in University of Alabama. They form part of the advanced undergraduate program of the universities. These programs have separate courses in Astro-Particle Cosmology, which we do not cover.

The students are expected to have completed their studies in intermediate physics (e.g. at the level of the textbook by Alonso \& Finn: Fundamental University Physics) and to have had the first course in Astronomy (using e.g. the textbook by Karttunen et al. Fundamental Astronomy). Since it is our experience that students often have gaps in their knowledge even at this level, we have tried to explain the key concepts starting from the basics. Thus the level of the book is adjusted according to our experience of teaching the courses over the years. We assume a background in calculus, differential equations, and vectors.

A modern cosmology course cannot be taught without General Relativity. It is not possible to understand gravity, in particular antigravity, without going into some details of the theory. This is a major obstacle since students at this level have had no exposure at all to General Relativity. On the other hand, a good introduction to General Relativity would consume the whole course. Here we have made a compromise where the theory has been explained as far as possible without the techniques of tensor calculus. An appeal to the Newtonian limit is made repeatedly, and calculation techniques familiar from Classical Mechanics (i.e., Lagrangians) are used. By skipping the Boxes one may avoid tensors almost totally in this course.

Our point of view on antigravity is that it is a manifestation of Einstein’s Lambda-term. As to the other key concept, dark matter, we take the position that it is likely to be cold and composed of weakly interacting massive particles which have so far not yet been discovered. It is likely that this view, LambdaCDM for short, will be dominant for some time to come, and even if it is finally modified or replaced by something else, it is necessary for the students to learn this theory.

Another shortcoming in the usual intermediate physics curriculum is the brevity of hydrodynamics. To help with this problem, we have carried out rather elementary derivations, in preparation for the discussion of small density perturbations in the early Universe. This is another key area necessary for the understanding of the processes of local physics.

The LambdaCDM has many consequences which have not been fully appreciated in older textbooks: the evolution of galaxies via multiple mergers of smaller dark matter halos, the key role played by supermassive black holes in the evolution of the stellar systems inside these halos, the population of intergalactic supermassive black holes which arise through the slingshot process subsequent to the mergers, etc. We have presented these new topics of the standard theory in considerable length.

Much of the cosmological observations today deal with correlations of galaxy distributions and of the anisotropies in the microwave background radiation. We spend considerable time in explaining the key concepts and also go to the analytical theory. Even though there are now wonderful numerical simulations of the evolution of cosmic structure, they may hide the deeper understanding of the related physics in the large numbers of parameters and assumptions necessary to set up such experiments. Ideally, we would like to test the fundamental theories using computer experiments as well as observations.

The evidence for dark matter has grown steadily over the years. We review the evidence for dark matter as well as the techniques of observing it. Especially, gravitational lensing has provided a new way of “seeing” the dark matter. We explain the gravitational lensing theory in considerable detail since it is likely to be the way of the future in studies of dark matter and galactic evolution.

The authors would like to thank the hospitality of the University of the West Indies, St.Augustine, Trinidad where the authors have met to coordinate their efforts and one of the authors (M.V.) did most of the writing. Similar meetings in St.Petersburg Russia, The University of Alabama, and Turku, Finland have been essential to this project, and support from the relevant institutions are gratefully acknowledged. Financial support for this work has been provided by the Academy of Finland through the project “Calculation of Orbits” and the United States National Science Foundation Grant AST020177 to Bevill State College in Fayette, Alabama. Authors thank Kimmo Innanen, Sverre Aarseth, Chris Flynn, Pekka Teerikorpi, Yuri Baryshev, Yuri Efremov, and Bill Saslaw for reading part of the manuscript and for valuable comments. The final version of the manuscript was put together by Sethanne Howard whose help has been invaluable. Besides the text itself, she has worked on most of the illustrations.

Tuorla, Finland

July 2005

Gene Byrd, Arthur Chernin, Mauri Valtonen
Authors
Gene G. Byrd received a B.S. degree from Texas A&M University in 1968. After receiving his PhD in 1974 on binary star formation and tidal interaction of galaxies from the University of Texas at Austin, he became a faculty member at the University of Alabama. A few years later he began his collaboration with Mauri Valtonen and in the 1990’s with Arthur Chernin. Dr. Byrd has served as Secretary and as Chair of the American Astronomical Society’s Division on Dynamical Astronomy and has helped organize several conferences, most recently “Order and Chaos in Stellar and Dynamical Systems” in St. Petersburg Russia (published by Astron. Soc. of the Pacific 2004).

Arthur D. Chernin graduated from the Leningrad Polytechnic Inst. in 1963 and got his PhD in 1969 from Ioffe Inst. and Dr. Sci. in 1979 from Pulkovo Observatory on cosmology and galaxy formation. He was a researcher at Ioffe Inst. In 1963–1982, then professor of theoretical physics at Herzen University in St. Petersburg. Since 1990 he has been at Sternberg Astronomical Inst. of Moscow University, sharing the interests of his co-authors in cosmology dark sector and the physics of galaxies. Dr. Chernin is a co-author of the book “Alexander Friedmann: the Man Who Made the Universe Expand” (Cambridge UP 1993, 2006) and several books in the Russian, Spanish and Japanese languages.

Mauri J. Valtonen graduated from the University of Helsinki in 1968, and did graduate work at the University of Cambridge in 1971–1974 on the three-body problem and the slingshot theory of radio sources. In 1976 he joined the Department of Physics and Astronomy at the University of Alabama. After returning to Finland, became Professor of Astronomy at the University of Turku. He has collaborated with his co-authors on cosmological topics Such as dark matter, simulations of disk galaxies and the binary black hole system OJ287. Dr. Valtonen is the co-author of the book, “The Three-body Problem” (Cambridge UP 2006) as well as a number of books in the Finnish language.
El autor
CHERNIN Artur Davidovich
Doktor fiziko-matematicheskikh nauk, professor Gosudarstvennogo astronomicheskogo instituta im. P. K. Shternberga Moskovskogo gosudarstvennogo universiteta. Oblast’ issledovanij — teoreticheskaya astrofizika i kosmologiya. Avtor (soavtor) bolee 200 nauchnikh statej i 7 knig, vishedshikh na russkom, anglijskom, ispanskom i yaponskom yazikakh; sredi nikh: «Zvezdi i fizika» (M.: URSS), «Kosmologiya i fizicheskij vakuum» (M.: URSS; v soavt. s I. V. Arkhangel’skoj i I. L. Rozentalem), «Aleksandr Aleksandrovich Fridman. Zhizn’ i deyatel’nost’» (M.: URSS; v soavt. s E. A. Troppom i V. Ya. Frenkelem), «Cosmology: Foundations and Frontiers» (M.: URSS; with Gene G. Byrd & Mauri J. Valtonen), «Fizika vremeni» (M.: URSS).