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= Dynamics of the Universe in Problems = | = Dynamics of the Universe in Problems = | ||
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+ | <p align="center" style="color:red; font-size: 16px">[[New_problems |''''' → NEW PROBLEMS ← ''''']]</p> | ||
+ | |||
+ | <p align="center">'''The total number of problems on this website.'''</p> | ||
+ | [[File:Numbers.png|center|164px]] | ||
=== About === | === About === | ||
− | There are | + | There are [https://www.google.com.ua/search?q=inurl%3Acosmology thousands] of websites with names that contain the term “cosmology”. Many of them are devoted to discussion of fundamental questions: whether there is life on Mars, what was there when there was nothing and the like. Our aim is much more modest. We present here an online living version of our book of problems on cosmology. |
=== Why problems, which and for whom?=== | === Why problems, which and for whom?=== | ||
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1.9 [[Thermo warm-up|Thermo warm-up]] | 1.9 [[Thermo warm-up|Thermo warm-up]] | ||
− | 2. [[:Category:Dynamics of the Expanding Universe|Dynamics of the Expanding Universe]] | + | 2. [[:Category:Dynamics of the Expanding Universe|'''Dynamics of the Expanding Universe''']] |
2.1 [[Homogeneous Universe|Homogeneous and isotropic Universe, Hubble's Law]] | 2.1 [[Homogeneous Universe|Homogeneous and isotropic Universe, Hubble's Law]] | ||
Line 57: | Line 62: | ||
2.2 [[Equations of General Relativity|Equations of General Relativity]] | 2.2 [[Equations of General Relativity|Equations of General Relativity]] | ||
− | 2.3 [[Friedman-Lemaitre-Robertson-Walker (FLRW) metric|Friedman- | + | 2.3 [[Friedman-Lemaitre-Robertson-Walker (FLRW) metric|Friedman-Lemaître-Robertson-Walker (FLRW) metric]] |
2.4 [[Expanding Universe: ordinarity, difficulties and paradoxes|Expanding Universe: ordinarity, difficulties and paradoxes]] | 2.4 [[Expanding Universe: ordinarity, difficulties and paradoxes|Expanding Universe: ordinarity, difficulties and paradoxes]] | ||
Line 77: | Line 82: | ||
2.9 [[Light and distances|Light and distances]] | 2.9 [[Light and distances|Light and distances]] | ||
− | 3. [[:Category:Dynamics of the Universe in the Big Bang Model|Dynamics of the Universe in the Big Bang Model]] | + | 3. [[:Category:Dynamics of the Universe in the Big Bang Model|'''Dynamics of the Universe in the Big Bang Model''']] |
3.1 [[General questions|General questions]] | 3.1 [[General questions|General questions]] | ||
Line 83: | Line 88: | ||
3.2 [[Solutions of Friedman equations in the Big Bang model|Solutions of Friedman equations in the Big Bang model]] | 3.2 [[Solutions of Friedman equations in the Big Bang model|Solutions of Friedman equations in the Big Bang model]] | ||
− | 3.3 [[ | + | 3.3 [[Polytropic equation of state|Polytropic equation of state]] |
− | 3.4 [[The | + | 3.4 [[The role of curvature in the dynamics of the Universe|The role of curvature in the dynamics of the Universe]] |
− | 3.5 [[ | + | 3.5 [[The Milne Universe|The Milne Universe]] |
− | 3.6 [[Energy conditions and the Raychaudhuri equation|Energy conditions and the Raychaudhuri equation]] | + | 3.6 [[Cosmological horizons|Cosmological horizons]] |
+ | |||
+ | 3.7 [[Energy conditions and the Raychaudhuri equation|Energy conditions and the Raychaudhuri equation]] | ||
3.6.1 [[Energy_conditions_and_the_Raychaudhuri_equation#Energy conditions|Energy conditions]] | 3.6.1 [[Energy_conditions_and_the_Raychaudhuri_equation#Energy conditions|Energy conditions]] | ||
Line 97: | Line 104: | ||
3.6.2 [[Energy_conditions_and_the_Raychaudhuri_equation#Sudden Future Singularities|Sudden future singularities]] | 3.6.2 [[Energy_conditions_and_the_Raychaudhuri_equation#Sudden Future Singularities|Sudden future singularities]] | ||
− | 3. | + | 3.8 [[Influence of cosmological expansion on local systems|Influence of cosmological expansion on local systems]] |
− | 3. | + | 3.9 [[Dynamics of the Universe in terms of redshift and conformal time|Dynamics of the Universe in terms of redshift and conformal time]] |
− | + | ||
− | + | ||
+ | 4. [[:Category:Black Holes|'''Black Holes''']] | ||
+ | |||
4.1 [[Technical warm-up|Technical warm-up]] | 4.1 [[Technical warm-up|Technical warm-up]] | ||
Line 143: | Line 150: | ||
4.3.8 [[Kerr_black_hole#Particles'_motion_in_the_equatorial_plane|Particles' motion in the equatorial plane]] | 4.3.8 [[Kerr_black_hole#Particles'_motion_in_the_equatorial_plane|Particles' motion in the equatorial plane]] | ||
− | 4.4 [[ | + | 4.4 [[Particles' motion in general black hole spacetimes|Particles' motion in general black hole spacetimes]] |
− | 4.4.1 [[ | + | 4.4.1 [[Particles' motion in general black hole spacetimes#Frames,_time_intervals_and_distances|Frames, time intervals and distances]] |
− | 4.4.2 [[Astrophysical black holes#Quantum_effects|Quantum effects]] | + | 4.4.2 [[Particles' motion in general black hole spacetimes#Fiducial_observers|Fiducial observers]] |
+ | |||
+ | 4.4.3 [[Particles' motion in general black hole spacetimes#Collision_of_particles:_general_relationships|Collision of particles: general relationships]] | ||
+ | |||
+ | 4.5 [[Astrophysical black holes|Astrophysical black holes]] | ||
+ | |||
+ | 4.5.1 [[Astrophysical black holes#Preliminary|Preliminary]] | ||
+ | |||
+ | 4.5.2 [[Astrophysical black holes#Quantum_effects|Quantum effects]] | ||
− | 5. [[:Category:Cosmic Microwave Background (CMB)|Cosmic Microwave Background (CMB)]] | + | 5. [[:Category:Cosmic Microwave Background (CMB)|'''Cosmic Microwave Background (CMB)''']] |
5.1 [[Thermodynamics of Black-Body Radiation|Thermodynamics of Black-Body Radiation]] | 5.1 [[Thermodynamics of Black-Body Radiation|Thermodynamics of Black-Body Radiation]] | ||
Line 163: | Line 178: | ||
5.6 [[Extras|Extras]] | 5.6 [[Extras|Extras]] | ||
− | 6. [[:Category:Thermodynamics of Universe|Thermodynamics of Universe]] | + | 6. [[:Category:Thermodynamics of Universe|'''Thermodynamics of Universe''']] |
6.1 [[Thermodynamical Properties of Elementary Particles|Thermodynamical Properties of Elementary Particles]] | 6.1 [[Thermodynamical Properties of Elementary Particles|Thermodynamical Properties of Elementary Particles]] | ||
Line 181: | Line 196: | ||
6.8 [[6_Extras|Extras]] | 6.8 [[6_Extras|Extras]] | ||
− | 10. [[:Category:Dark Matter|Dark Matter]] | + | 7. [[:Category:Perturbation theory in cosmology|'''Perturbation theory in cosmology''']] |
+ | |||
+ | 7.1 [[Non relativistic small perturbation theory|Non relativistic small perturbation theory]] | ||
+ | |||
+ | 7.2 [[Introduction to relativistic theory of small perturbations|Introduction to relativistic theory of small perturbations]] | ||
+ | |||
+ | 7.2.1 [[Introduction to relativistic theory of small perturbations#Perturbations on flat background|Perturbations on flat background]] | ||
+ | |||
+ | 7.2.2 [[Introduction to relativistic theory of small perturbations#Metrics perturbations, coordinates transforms and perturbed energy-momentum tensor|Metrics perturbations, coordinates transforms and perturbed energy--momentum tensor]] | ||
+ | |||
+ | 7.3 [[Expansion of cosmological perturbations in helicities|Expansion of cosmological perturbations in helicities]] | ||
+ | |||
+ | 7.3.1 [[Expansion_of_cosmological_perturbations_in_helicities#Scalar_perturbations_in_conformal_Newtonian_gauge|Scalar perturbations in conformal Newtonian gauge]] | ||
+ | |||
+ | 7.3.2 [[Expansion_of_cosmological_perturbations_in_helicities#Evolution_of_vector_and_tensor_perturbations|Evolution of vector and tensor perturbations]] | ||
+ | |||
+ | 7.4 [[CMB anisotropy|CMB anisotropy]] | ||
+ | |||
+ | 7.5 [[Initial perturbations in the Universe|Initial perturbations in the Universe]] | ||
+ | |||
+ | 7.5.1 [[Initial perturbations in the Universe#Fluctuations power spectrum: non-relativistic approach|Fluctuations power spectrum: non-relativistic approach]] | ||
+ | |||
+ | |||
+ | 8. [[:Category:Inflation|'''Inflation''']] | ||
+ | |||
+ | 8.1 [[Problems of the Hot Universe (the Big Bang Model)|Problems of the Hot Universe (the Big Bang Model)]] | ||
+ | |||
+ | 8.1.1 [[Problems of the Hot Universe (the Big Bang Model)#The Horizon Problem|The Horizon Problem]] | ||
+ | |||
+ | 8.1.2 [[Problems of the Hot Universe (the Big Bang Model)#The Flatness Problem|The Flatness Problem]] | ||
+ | |||
+ | 8.1.3 [[Problems of the Hot Universe (the Big Bang Model)#The Entropy Problem|The Entropy Problem]] | ||
+ | |||
+ | 8.1.4 [[Problems of the Hot Universe (the Big Bang Model)#The Primary Inhomogeneities Problem|The Primary Inhomogeneities Problem]] | ||
+ | |||
+ | 8.2 [[Cosmological Inflation: The Canonic Theory|Cosmological Inflation: The Canonic Theory]] | ||
+ | |||
+ | 8.2.1 [[Cosmological Inflation: The Canonic Theory#Scalar Field In Cosmology|Scalar Field In Cosmology]] | ||
+ | |||
+ | 8.2.2 [[Cosmological Inflation: The Canonic Theory#Inflationary Introduction|Inflationary Introduction]] | ||
+ | |||
+ | 8.2.3 [[Cosmological Inflation: The Canonic Theory#Solution of the Hot Big Bang Theory Problems|Solution of the Hot Big Bang Theory Problems]] | ||
+ | |||
+ | 8.3 [[Different Models of Inflation|Different Models of Inflation]] | ||
+ | |||
+ | 8.3.1 [[Different Models of Inflation#Chaotic Inflation (The Inflation with Power Law Potential)|Chaotic Inflation (The Inflation with Power Law Potential)]] | ||
+ | |||
+ | 8.3.2 [[Different Models of Inflation#The Novel Inflation (the Inflation Near Minimum of the Potntial)|The Novel Inflation (the Inflation Near Minimum of the Potntial)]] | ||
+ | |||
+ | 8.3.3 [[Different Models of Inflation#Inflation with Exponential Potential (the Power Law Inflation)|Inflation with Exponential Potential (the Power Law Inflation)]] | ||
+ | |||
+ | 8.3.4 [[Different Models of Inflation#The Hybrid Inflation|The Hybrid Inflation]] | ||
+ | |||
+ | 8.3.5 [[Different Models of Inflation#Other Types of Inflation|Other Types of Inflation]] | ||
+ | |||
+ | 9. [[:Category:Dark Energy|'''Dark Energy''']] | ||
+ | |||
+ | 9.1 [[The Cosmological Constant|The Cosmological Constant]] | ||
+ | |||
+ | 9.2 [[Geometry and Destiny|Geometry and Destiny]] | ||
+ | |||
+ | 9.3 [[Time-dependent Cosmological Constant|Time-dependent Cosmological Constant]] | ||
+ | |||
+ | 9.4 [[Static Einstein's Universe|Static Einstein's Universe]] | ||
+ | |||
+ | 9.5 [[Dynamical Forms of Dark Energy|Dynamical Forms of Dark Energy]] | ||
+ | |||
+ | 9.5.1 [[Dynamical Forms of Dark Energy#The Quintessence|The Quintessence]] | ||
+ | |||
+ | 9.5.2 [[Dynamical Forms of Dark Energy#The K-essence|The K-essence]] | ||
+ | |||
+ | 9.5.3 [[Dynamical Forms of Dark Energy#Phantom Energy|Phantom Energy]] | ||
+ | |||
+ | 9.5.4 [[Dynamical Forms of Dark Energy#Disintegration of Bound Structures|Disintegration of Bound Structures]] | ||
+ | |||
+ | 9.5.5 [[Dynamical Forms of Dark Energy#Big Rip, Pseudo Rip, Little Rip|Big Rip, Pseudo Rip, Little Rip]] | ||
+ | |||
+ | 9.5.6 [[Dynamical Forms of Dark Energy#The Statefinder|The Statefinder]] | ||
+ | |||
+ | 9.5.7 [[Dynamical Forms of Dark Energy#Crossing the Phantom Divide|Crossing the Phantom Divide]] | ||
+ | |||
+ | 9.6 [[Lost and Found|Lost and Found]] | ||
+ | |||
+ | 9.7 [[Single Scalar Cosmology|Single Scalar Cosmology]] | ||
+ | |||
+ | 10. [[:Category:Dark Matter|'''Dark Matter''']] | ||
10.1 [[Observational Evidence of the Dark matter Existence|Observational Evidence of the Dark matter Existence]] | 10.1 [[Observational Evidence of the Dark matter Existence|Observational Evidence of the Dark matter Existence]] | ||
Line 201: | Line 301: | ||
10.7 [[The Dark Stars|The Dark Stars]] | 10.7 [[The Dark Stars|The Dark Stars]] | ||
− | + | 11. [[:Category:Interactions in the Dark Sector|'''Interactions in the Dark Sector''']] | |
− | + | 11.1 [[Physical mechanism of energy exchange|Physical mechanism of energy exchange]] | |
− | + | 11.2 [[Phenomenology of interacting models|Phenomenology of interacting models]] | |
− | + | 11.3 [[Simple linear models|Simple linear models]] | |
− | + | 11.4 [[Cosmological models with a change of the direction of energy transfer|Cosmological models with a change of the direction of energy transfer]] | |
− | + | 11.5 [[Non-linear interaction in the dark sector|Non-linear interaction in the dark sector]] | |
+ | |||
+ | 11.6 [[Phase space structure of models with interaction|Phase space structure of models with interaction]] | ||
+ | |||
+ | 11.7 [[Peculiarity of dynamics of scalar field coupled to dark matter|Peculiarity of dynamics of scalar field coupled to dark matter]] | ||
+ | |||
+ | 11.7.1 [[Peculiarity of dynamics of scalar field coupled to dark matter#Interacting quintessence model|Interacting quintessence model]] | ||
+ | |||
+ | 11.7.2 [[Peculiarity of dynamics of scalar field coupled to dark matter#Interacting phantom|Interacting phantom]] | ||
+ | |||
+ | 11.8 [[Realization of interaction in the dark sector|Realization of interaction in the dark sector]] | ||
+ | |||
+ | 11.8.1 [[Realization of interaction in the dark sector#Vacuum decay into cold dark matter|Vacuum decay into cold dark matter]] | ||
+ | |||
+ | 11.8.2 [[Realization of interaction in the dark sector#Time-dependent cosmological "constant"|Time-dependent cosmological "constant"]] | ||
+ | |||
+ | 11.9 [[Statefinder parameters for interacting dark energy and cold dark matter|Statefinder parameters for interacting dark energy and cold dark matter]] | ||
+ | |||
+ | 11.10 [[Interacting holographic dark energy|Interacting holographic dark energy]] | ||
+ | |||
+ | 11.11 [[Transient acceleration|Transient acceleration]] | ||
+ | |||
+ | 12. [[:Category:Standard Cosmological Model|'''Standard Cosmological Model''']] | ||
+ | |||
+ | 12.1 [[Characteristic Parameters and Scales|Characteristic Parameters and Scales]] | ||
+ | |||
+ | 12.2 [[Evolution of Universe|Evolution of Universe]] | ||
− | + | 13. [[:Category:Weak field limit and gravitational waves|'''Weak field limit and gravitational waves''']] | |
− | + | 13.1 [[Motivation and symmetries / Introduction|Motivation and symmetries / Introduction]] | |
− | + | 13.2 [[Linearized Einstein equations|Linearized Einstein equations]] | |
+ | |||
+ | 13.3 [[Gauge transformations and degrees of freedom|Gauge transformations and degrees of freedom]] | ||
+ | |||
+ | 13.4 [[Wave equation|Wave equation]] | ||
+ | |||
+ | 13.5 [[Transverse traceless gauge|Transverse traceless gauge]] | ||
+ | |||
+ | 13.6 [[Gravitational waves and matter|Gravitational waves and matter]] | ||
+ | |||
+ | 13.7 [[Energy of gravitational waves|Energy of gravitational waves]] | ||
+ | |||
+ | 13.8 [[Binary systems|Binary systems]] | ||
+ | |||
+ | 13.9 [[Gravitational Waves: scale of the phenomenon|Gravitational Waves: scale of the phenomenon]] | ||
+ | |||
+ | 13.10 [[Generation and detection of gravitational waves|Generation and detection of gravitational waves]] | ||
+ | |||
+ | 14. [[:Category:Observational Cosmology|'''Observational cosmology''']] | ||
+ | |||
+ | 14.1 [[Point gravitational lenses|Point gravitational lenses]] | ||
+ | |||
+ | 14.2 [[Microlensing and Weak Lensing|Microlensing and weak lensing]] | ||
+ | |||
+ | 15. [[:Category:Holographic Universe|'''Holographic Universe''']] | ||
+ | |||
+ | 15.1 [[Information, Entropy and Holographic Screen|Information, Entropy and Holographic Screen]] | ||
+ | |||
+ | 16. [[:Category:Horizons|'''Horizons''']] | ||
+ | |||
+ | 16.1 [[Simple English|Simple English]] | ||
+ | |||
+ | 16.2 [[Simple Math|Simple Math]] | ||
+ | |||
+ | 16.3 [[Composite Models|Composite Models]] | ||
+ | |||
+ | 16.4 [[Causal Structure|Causal Structure]] | ||
+ | |||
+ | 16.5 [[Conformal diagrams: stationary black holes|Conformal diagrams: stationary black holes]] | ||
+ | |||
+ | 16.5.1 [[Conformal diagrams: stationary black holes#Schwarzschild-Kruskal black hole solution|Schwarzschild-Kruskal black hole solution]] | ||
+ | |||
+ | 16.5.2 [[Conformal diagrams: stationary black holes#Other spherically symmetric black holes|Other spherically symmetric black holes]] | ||
+ | |||
+ | 16.6 [[Hubble sphere|Hubble sphere]] | ||
+ | |||
+ | 16.7 [[Proper horizons|Proper horizons]] | ||
+ | |||
+ | 16.8 [[Inflation|Inflation]] | ||
+ | |||
+ | 16.9 [[Holography|Holography]] | ||
+ | |||
+ | 17. [[:Category:Deceleration Parameter|'''Deceleration Parameter''']] | ||
+ | |||
+ | 18. [[:Category:Quantum Cosmology|'''Quantum Cosmology''']] |
Latest revision as of 17:38, 23 February 2015
Contents
Dynamics of the Universe in Problems
The total number of problems on this website.
About
There are thousands of websites with names that contain the term “cosmology”. Many of them are devoted to discussion of fundamental questions: whether there is life on Mars, what was there when there was nothing and the like. Our aim is much more modest. We present here an online living version of our book of problems on cosmology.
Why problems, which and for whom?
The only way to rise above the “popular” level in any science is to master its alphabet, that is, to learn to solve problems, even if most simple at the beginning. To our best knowledge, there are no problem books on cosmology yet, that would include its spectacular recent achievements. Of course, most of excellent modern textbooks on cosmology include problems. However, a reader, exhausted by high theory, may often be thwarted by the lack of time and strength to solve them.
You can familiarize oneself with the modern portrayal of the dynamics of the Universe, including the latest achievements of cosmology, by solving problems from the start. The perseverant will traverse the thorny path of cosmology’s evolution from the traditional Big Bang model to the presently universally accepted Standard Cosmological Model. It is based on the revolutionary discovery of accelerated expansion of the Universe, made at the very end of the last century. The attempts to explain such an unexpected observation led to fundamental reconstruction of the view on the evolution of the Universe that was formed in the XX century.
One only has to be acquainted with the basics of Special and General Relativities and the theory of elementary particles in order to start solving problems. We want to show that even this minimal knowledge is sufficient to be able to solve a very wide range of cosmological problems, and moreover, to understand the essence of difficulties that are encountered by modern cosmology.
No generation of Homo sapiens could withstand the temptation to claim that the true understanding of the nature of the Universe is (almost?) within its grasp. The current generation is not an exception, of course, naturally assuming it has better reason to believe so than ever before. We hope to give our reader the means to evaluate objectively whether this is true or not by himself.
Second life online
We published the first edition of the problem book a couple of years ago, in Russian. However, a printed book, even not taking into account the language, has its obvious drawbacks in itself. The audience is limited by the number of copies printed. The inevitable misprints and errors cannot be corrected – the errors in classical problem books on physics are known to be sometimes corrected in the fifteenth edition. But the main problem that almost immediately manifested itself was that the content of the book with pretentious title “Modern Cosmology” was getting out of date by leaps and bounds. New sections and subsections demanded to be created and populated with problems. The online living problem book is the solution we have come to.
At the moment we have about 1500 problems, almost all of them with solutions, and we hope to bring them online by the fall of 2012. We tried to make references to the authors of problems whenever possible and would be happy to add the references that might still be missing. Some problems have already acquired the status of folklore and their authorship is hard to determine. We welcome all comments, suggestions and corrections to the formulations of problems and their solutions, but most valuable to us would be new problems suggested by the community.
Good luck
Finally, we hope that after getting to grip with the problems our reader not only preserves his interest to cosmology, but tries to make the next step: read original papers. If this transition is overcome seamlessly, we will have achieved our goal.
Welcome!
CONTENTS
1.1 Astronomy "before the Common Era" 1.2 Quantities large and small 1.3 Geometric warm-up 1.4 Astrophysical warm-up 1.5 Planck scales and fundamental constants $c$, $G$, $\hbar$ 1.6 Gravity 1.7 Forest for the trees 1.8 Life on Mars? 1.8.1 Fine-tuning of the Universe 1.9 Thermo warm-up
2. Dynamics of the Expanding Universe
2.1 Homogeneous and isotropic Universe, Hubble's Law 2.2 Equations of General Relativity 2.3 Friedman-Lemaître-Robertson-Walker (FLRW) metric 2.4 Expanding Universe: ordinarity, difficulties and paradoxes 2.4.1 Warm-up 2.4.2 The tethered galaxy problem 2.4.3 Cosmological redshift 2.5 Friedman equations 2.6 Newtonian cosmology 2.7 Energy balance in an expanding Universe 2.8 Cosmography 2.9 Light and distances
3. Dynamics of the Universe in the Big Bang Model
3.1 General questions 3.2 Solutions of Friedman equations in the Big Bang model 3.3 Polytropic equation of state 3.4 The role of curvature in the dynamics of the Universe 3.5 The Milne Universe 3.6 Cosmological horizons 3.7 Energy conditions and the Raychaudhuri equation 3.6.1 Energy conditions 3.6.2 Raychaudhuri equation 3.6.2 Sudden future singularities 3.8 Influence of cosmological expansion on local systems 3.9 Dynamics of the Universe in terms of redshift and conformal time
4. Black Holes
4.1 Technical warm-up 4.1.1 Uniformly accelerated observer, Rindler metric 4.1.2 Metric in curved spacetime 4.2 Schwarzschild black hole 4.2.1 Simple problems 4.2.2 Symmetries and integrals of motion 4.2.3 Radial motion 4.2.4 Blackness of black holes 4.2.5 Orbital motion, effective potential 4.2.6 Miscellaneous problems 4.2.7 Different coordinates, maximal extension 4.3 Kerr black hole 4.3.1 General axially symmetric metric 4.3.2 Limiting cases 4.3.3 Horizons and singularity 4.3.4 Stationary limit 4.3.5 Ergosphere and the Penrose process 4.3.6 Integrals of motion 4.3.7 The laws of mechanics of black holes 4.3.8 Particles' motion in the equatorial plane 4.4 Particles' motion in general black hole spacetimes 4.4.1 Frames, time intervals and distances 4.4.2 Fiducial observers 4.4.3 Collision of particles: general relationships 4.5 Astrophysical black holes 4.5.1 Preliminary 4.5.2 Quantum effects
5. Cosmic Microwave Background (CMB)
5.1 Thermodynamics of Black-Body Radiation 5.2 Time Evolution of CMB 5.3 Statistical properties of CMB 5.4 Primary anisotropy of CMB 5.5 CMB interaction with other components 5.6 Extras
6.1 Thermodynamical Properties of Elementary Particles 6.2 Thermodynamics of Non-Relativistic Gas 6.3 Entropy of Expanding Universe 6.4 Connection between Temperature and Redshift 6.5 Peculiarities of Thermodynamics in Early Universe 6.6 The Saha equation 6.7 Primary Nucleosynthesis 6.8 Extras
7. Perturbation theory in cosmology
7.1 Non relativistic small perturbation theory 7.2 Introduction to relativistic theory of small perturbations 7.2.1 Perturbations on flat background 7.2.2 Metrics perturbations, coordinates transforms and perturbed energy--momentum tensor 7.3 Expansion of cosmological perturbations in helicities 7.3.1 Scalar perturbations in conformal Newtonian gauge 7.3.2 Evolution of vector and tensor perturbations 7.4 CMB anisotropy 7.5 Initial perturbations in the Universe 7.5.1 Fluctuations power spectrum: non-relativistic approach
8. Inflation
8.1 Problems of the Hot Universe (the Big Bang Model) 8.1.1 The Horizon Problem 8.1.2 The Flatness Problem 8.1.3 The Entropy Problem 8.1.4 The Primary Inhomogeneities Problem 8.2 Cosmological Inflation: The Canonic Theory 8.2.1 Scalar Field In Cosmology 8.2.2 Inflationary Introduction 8.2.3 Solution of the Hot Big Bang Theory Problems 8.3 Different Models of Inflation 8.3.1 Chaotic Inflation (The Inflation with Power Law Potential) 8.3.2 The Novel Inflation (the Inflation Near Minimum of the Potntial) 8.3.3 Inflation with Exponential Potential (the Power Law Inflation) 8.3.4 The Hybrid Inflation 8.3.5 Other Types of Inflation
9. Dark Energy
9.1 The Cosmological Constant 9.2 Geometry and Destiny 9.3 Time-dependent Cosmological Constant 9.4 Static Einstein's Universe 9.5 Dynamical Forms of Dark Energy 9.5.1 The Quintessence 9.5.2 The K-essence 9.5.3 Phantom Energy 9.5.4 Disintegration of Bound Structures 9.5.5 Big Rip, Pseudo Rip, Little Rip 9.5.6 The Statefinder 9.5.7 Crossing the Phantom Divide 9.6 Lost and Found 9.7 Single Scalar Cosmology
10. Dark Matter
10.1 Observational Evidence of the Dark matter Existence 10.2 ANONIMOUS 10.3 Dark Matter Halo 10.4 Candidates for Dark Matter Particles 10.4.1 Standard Model Particles as Dark Matter Candidates 10.4.2 Supersymmetric Candidate Particles 10.5 Dark Matter Detection 10.6 The Dark Matter in the Solar System 10.7 The Dark Stars
11. Interactions in the Dark Sector
11.1 Physical mechanism of energy exchange 11.2 Phenomenology of interacting models 11.3 Simple linear models 11.4 Cosmological models with a change of the direction of energy transfer 11.5 Non-linear interaction in the dark sector 11.6 Phase space structure of models with interaction 11.7 Peculiarity of dynamics of scalar field coupled to dark matter 11.7.1 Interacting quintessence model 11.7.2 Interacting phantom 11.8 Realization of interaction in the dark sector 11.8.1 Vacuum decay into cold dark matter 11.8.2 Time-dependent cosmological "constant" 11.9 Statefinder parameters for interacting dark energy and cold dark matter 11.10 Interacting holographic dark energy 11.11 Transient acceleration
12. Standard Cosmological Model
12.1 Characteristic Parameters and Scales 12.2 Evolution of Universe
13. Weak field limit and gravitational waves
13.1 Motivation and symmetries / Introduction 13.2 Linearized Einstein equations 13.3 Gauge transformations and degrees of freedom 13.4 Wave equation 13.5 Transverse traceless gauge 13.6 Gravitational waves and matter 13.7 Energy of gravitational waves 13.8 Binary systems 13.9 Gravitational Waves: scale of the phenomenon 13.10 Generation and detection of gravitational waves
14.1 Point gravitational lenses 14.2 Microlensing and weak lensing
15.1 Information, Entropy and Holographic Screen
16. Horizons
16.1 Simple English 16.2 Simple Math 16.3 Composite Models 16.4 Causal Structure 16.5 Conformal diagrams: stationary black holes 16.5.1 Schwarzschild-Kruskal black hole solution 16.5.2 Other spherically symmetric black holes 16.6 Hubble sphere 16.7 Proper horizons 16.8 Inflation 16.9 Holography