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                        "user": "Cosmo All",
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                        "*": "= Dynamics of the Universe in Problems =\n\n<p align=\"center\" style=\"color:red; font-size: 16px\">[[New_problems |''''' &rarr; NEW PROBLEMS &larr; ''''']]</p>\n\n<p align=\"center\">'''The total number of problems on this website.'''</p>\n[[File:Numbers.png\u200e|center|164px]]\n\n\n=== About ===\n\nThere are [https://www.google.com.ua/search?q=inurl%3Acosmology thousands] of websites with names that contain the term \u201ccosmology\u201d. 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.\n\n=== Why problems, which and for whom?===\nThe only way to rise above the \u201cpopular\u201d 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.\n\nYou 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\u2019s 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. \n\nOne 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.\n\nNo 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.\n\n=== Second life online===\nWe 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 \u2013 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 \u201cModern Cosmology\u201d 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.\n\nAt 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.\n\n=== Good luck===\nFinally, 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.\n\nWelcome!\n\n\n----\n\n= CONTENTS =\n1. [[:Category:Cosmo warm-up|'''Cosmo warm-up''']]\n\n   1.1 [[Astronomy \"before the Common Era\"|Astronomy \"before the Common Era\"]]\n   \n   1.2 [[Quantities large and small|Quantities large and small]]\n   \n   1.3 [[Geometric warm-up|Geometric warm-up]]\n   \n   1.4 [[Astrophysical warm-up|Astrophysical warm-up]]\n   \n   1.5 [[Planck scales and fundamental constants|Planck scales and fundamental constants  $c$, $G$, $\\hbar$]]\n   \n   1.6 [[Gravity|Gravity]]\n   \n   1.7 [[Forest for the trees|Forest for the trees]]\n   \n   1.8 [[Life on Mars?|Life on Mars?]]\n   \n       1.8.1 [[Life on Mars?#Fine-tuning of the Universe|Fine-tuning of the Universe]]\n   \n   1.9 [[Thermo warm-up|Thermo warm-up]]\n\n2. [[:Category:Dynamics of the Expanding Universe|'''Dynamics of the Expanding Universe''']]\n\n   2.1 [[Homogeneous Universe|Homogeneous and isotropic Universe, Hubble's Law]]\n   \n   2.2 [[Equations of General Relativity|Equations of General Relativity]]\n   \n   2.3 [[Friedman-Lemaitre-Robertson-Walker (FLRW) metric|Friedman-Lema\u00eetre-Robertson-Walker (FLRW) metric]]\n   \n   2.4 [[Expanding Universe: ordinarity, difficulties and paradoxes|Expanding Universe: ordinarity, difficulties and paradoxes]]\n   \n       2.4.1 [[Expanding_Universe:_ordinarity,_difficulties_and_paradoxes#Warm-up|Warm-up]]\n       \n       2.4.2 [[Expanding_Universe:_ordinarity,_difficulties_and_paradoxes#The_tethered_galaxy_problem|The tethered galaxy problem]]\n   \n       2.4.3 [[Expanding_Universe:_ordinarity,_difficulties_and_paradoxes#Cosmological_redshift|Cosmological redshift]]\n   \n   2.5 [[Friedman equations|Friedman equations]]\n   \n   2.6 [[Newtonian cosmology|Newtonian cosmology]]\n   \n   2.7 [[Energy balance in an expanding Universe|Energy balance in an expanding Universe]]\n   \n   2.8 [[Cosmography|Cosmography]]\n   \n   2.9 [[Light and distances|Light and distances]]\n\n3. [[:Category:Dynamics of the Universe in the Big Bang Model|'''Dynamics of the Universe in the Big Bang Model''']]\n   \n   3.1 [[General questions|General questions]]\n   \n   3.2 [[Solutions of Friedman equations in the Big Bang model|Solutions of Friedman equations in the Big Bang model]]\n   \n   3.3 [[Polytropic equation of state|Polytropic equation of state]]\n   \n   3.4 [[The role of curvature in the dynamics of the Universe|The role of curvature in the dynamics of the Universe]]\n   \n   3.5 [[The Milne Universe|The Milne Universe]]\n   \n   3.6 [[Cosmological horizons|Cosmological horizons]]\n   \n   3.7 [[Energy conditions and the Raychaudhuri equation|Energy conditions and the Raychaudhuri equation]]\n   \n       3.6.1 [[Energy_conditions_and_the_Raychaudhuri_equation#Energy conditions|Energy conditions]]\n   \n       3.6.2 [[Energy_conditions_and_the_Raychaudhuri_equation#Raychaudhuri equation|Raychaudhuri equation]]\n   \n       3.6.2 [[Energy_conditions_and_the_Raychaudhuri_equation#Sudden Future Singularities|Sudden future singularities]]\n   \n   3.8 [[Influence of cosmological expansion on local systems|Influence of cosmological expansion on local systems]]\n   \n   3.9 [[Dynamics of the Universe in terms of redshift and conformal time|Dynamics of the Universe in terms of redshift and conformal time]]\n\n4. [[:Category:Black Holes|'''Black Holes''']]\n   \n   4.1 [[Technical warm-up|Technical warm-up]]\n   \n       4.1.1 [[Technical_warm-up#Uniformly_accelerated_observer,_Rindler_metric|Uniformly accelerated observer, Rindler metric]]\n   \n       4.1.2 [[Technical_warm-up#Metric_in_curved_space-time|Metric in curved spacetime]]\n   \n   4.2 [[Schwarzschild black hole|Schwarzschild black hole]]\n   \n       4.2.1 [[Schwarzschild_black_hole#Simple_problems|Simple problems]]\n   \n       4.2.2 [[Schwarzschild_black_hole#Symmetries_and_integrals_of_motion|Symmetries and integrals of motion]]\n   \n       4.2.3 [[Schwarzschild_black_hole#Radial_motion|Radial motion]]\n   \n       4.2.4 [[Schwarzschild_black_hole#Blackness_of_black_holes|Blackness of black holes]]\n   \n       4.2.5 [[Schwarzschild_black_hole#Orbital_motion,_effective_potential|Orbital motion, effective potential]]\n   \n       4.2.6 [[Schwarzschild_black_hole#Miscellaneous_problems|Miscellaneous problems]]\n   \n       4.2.7 [[Schwarzschild_black_hole#Different_coordinates,_maximal_extension|Different coordinates, maximal extension]]\n   \n   4.3 [[Kerr black hole|Kerr black hole]]\n   \n       4.3.1 [[Kerr_black_hole#General_axially_symmetric_metric|General axially symmetric metric]]\n   \n       4.3.2 [[Kerr_black_hole#Limiting_cases|Limiting cases]]\n   \n       4.3.3 [[Kerr_black_hole#Horizons_and_singularity|Horizons and singularity]]\n   \n       4.3.4 [[Kerr_black_hole#Stationary_limit|Stationary limit]]\n   \n       4.3.5 [[Kerr_black_hole#Ergosphere_and_the_Penrose_process|Ergosphere and the Penrose process]]\n   \n       4.3.6 [[Kerr_black_hole#Integrals_of_motion|Integrals of motion]]\n   \n       4.3.7 [[Kerr_black_hole#The_laws_of_mechanics_of_black_holes|The laws of mechanics of black holes]]\n   \n       4.3.8 [[Kerr_black_hole#Particles'_motion_in_the_equatorial_plane|Particles' motion in the equatorial plane]]   \n   \n   4.4 [[Particles' motion in general black hole spacetimes|Particles' motion in general black hole spacetimes]]\n   \n       4.4.1 [[Particles' motion in general black hole spacetimes#Frames,_time_intervals_and_distances|Frames, time intervals and distances]]\n   \n       4.4.2 [[Particles' motion in general black hole spacetimes#Fiducial_observers|Fiducial observers]]\n   \n       4.4.3 [[Particles' motion in general black hole spacetimes#Collision_of_particles:_general_relationships|Collision of particles: general relationships]]\n   \n   4.5 [[Astrophysical black holes|Astrophysical black holes]]\n   \n       4.5.1 [[Astrophysical black holes#Preliminary|Preliminary]]\n   \n       4.5.2 [[Astrophysical black holes#Quantum_effects|Quantum effects]]\n\n5. [[:Category:Cosmic Microwave Background (CMB)|'''Cosmic Microwave Background (CMB)''']]\n\n   5.1 [[Thermodynamics of Black-Body Radiation|Thermodynamics of Black-Body Radiation]]\n      \n   5.2 [[Time Evolution of CMB|Time Evolution of CMB]]\n   \n   5.3 [[Statistical properties of CMB|Statistical properties of CMB]]\n   \n   5.4 [[Primary anisotropy of CMB|Primary anisotropy of CMB]]\n   \n   5.5 [[CMB interaction with other components|CMB interaction with other components]]\n   \n   5.6 [[Extras|Extras]]\n\n6. [[:Category:Thermodynamics of Universe|'''Thermodynamics of Universe''']]\n\n   6.1 [[Thermodynamical Properties of Elementary Particles|Thermodynamical Properties of Elementary Particles]]\n      \n   6.2 [[Thermodynamics of Non-Relativistic Gas|Thermodynamics of Non-Relativistic Gas]]\n   \n   6.3 [[Entropy of Expanding Universe|Entropy of Expanding Universe]]\n   \n   6.4 [[Connection between Temperature and Redshift|Connection between Temperature and Redshift]]\n   \n   6.5 [[Peculiarities of Thermodynamics in Early Universe|Peculiarities of Thermodynamics in Early Universe]]\n   \n   6.6 [[The Saha equation|The Saha equation]]\n   \n   6.7 [[Primary Nucleosynthesis|Primary Nucleosynthesis]]\n   \n   6.8 [[6_Extras|Extras]]\n\n7. [[:Category:Perturbation theory in cosmology|'''Perturbation theory in cosmology''']]\n\n   7.1 [[Non relativistic small perturbation theory|Non relativistic small perturbation theory]]\n   \n   7.2 [[Introduction to relativistic theory of small perturbations|Introduction to relativistic theory of small perturbations]]\n   \n       7.2.1 [[Introduction to relativistic theory of small perturbations#Perturbations on flat background|Perturbations on flat background]]\n   \n       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]]\n   \n   7.3 [[Expansion of cosmological perturbations in helicities|Expansion of cosmological perturbations in helicities]]\n   \n       7.3.1 [[Expansion_of_cosmological_perturbations_in_helicities#Scalar_perturbations_in_conformal_Newtonian_gauge|Scalar perturbations in conformal Newtonian gauge]]\n   \n       7.3.2 [[Expansion_of_cosmological_perturbations_in_helicities#Evolution_of_vector_and_tensor_perturbations|Evolution of vector and tensor perturbations]]\n   \n   7.4 [[CMB anisotropy|CMB anisotropy]]\n   \n   7.5 [[Initial perturbations in the Universe|Initial perturbations in the Universe]]\n   \n       7.5.1 [[Initial perturbations in the Universe#Fluctuations power spectrum: non-relativistic approach|Fluctuations power spectrum: non-relativistic approach]]\n\n\n8. [[:Category:Inflation|'''Inflation''']]\n\n   8.1 [[Problems of the Hot Universe (the Big Bang Model)|Problems of the Hot Universe (the Big Bang Model)]]\n   \n       8.1.1 [[Problems of the Hot Universe (the Big Bang Model)#The Horizon Problem|The Horizon Problem]]\n       \n       8.1.2 [[Problems of the Hot Universe (the Big Bang Model)#The Flatness Problem|The Flatness Problem]]\n       \n       8.1.3 [[Problems of the Hot Universe (the Big Bang Model)#The Entropy Problem|The Entropy Problem]]\n       \n       8.1.4 [[Problems of the Hot Universe (the Big Bang Model)#The Primary Inhomogeneities Problem|The Primary Inhomogeneities Problem]]\n      \n   8.2 [[Cosmological Inflation: The Canonic Theory|Cosmological Inflation: The Canonic Theory]]\n   \n       8.2.1 [[Cosmological Inflation: The Canonic Theory#Scalar Field In Cosmology|Scalar Field In Cosmology]]\n   \n       8.2.2 [[Cosmological Inflation: The Canonic Theory#Inflationary Introduction|Inflationary Introduction]]\n   \n       8.2.3 [[Cosmological Inflation: The Canonic Theory#Solution of the Hot Big Bang Theory Problems|Solution of the Hot Big Bang Theory Problems]]\n   \n   8.3 [[Different Models of Inflation|Different Models of Inflation]]\n   \n       8.3.1 [[Different Models of Inflation#Chaotic Inflation (The Inflation with Power Law Potential)|Chaotic Inflation (The Inflation with Power Law Potential)]]\n   \n       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)]]\n   \n       8.3.3 [[Different Models of Inflation#Inflation with Exponential Potential (the Power Law Inflation)|Inflation with Exponential Potential (the Power Law Inflation)]]\n   \n       8.3.4 [[Different Models of Inflation#The Hybrid Inflation|The Hybrid Inflation]]\n   \n       8.3.5 [[Different Models of Inflation#Other Types of Inflation|Other Types of Inflation]]\n   \n9. [[:Category:Dark Energy|'''Dark Energy''']]\n\n   9.1 [[The Cosmological Constant|The Cosmological Constant]]\n      \n   9.2 [[Geometry and Destiny|Geometry and Destiny]]\n   \n   9.3 [[Time-dependent Cosmological Constant|Time-dependent Cosmological Constant]]\n   \n   9.4 [[Static Einstein's Universe|Static Einstein's Universe]]\n   \n   9.5 [[Dynamical Forms of Dark Energy|Dynamical Forms of Dark Energy]]\n   \n       9.5.1 [[Dynamical Forms of Dark Energy#The Quintessence|The Quintessence]]\n       \n       9.5.2 [[Dynamical Forms of Dark Energy#The K-essence|The K-essence]]\n       \n       9.5.3 [[Dynamical Forms of Dark Energy#Phantom Energy|Phantom Energy]]\n       \n       9.5.4 [[Dynamical Forms of Dark Energy#Disintegration of Bound Structures|Disintegration of Bound Structures]]\n       \n       9.5.5 [[Dynamical Forms of Dark Energy#Big Rip, Pseudo Rip, Little Rip|Big Rip, Pseudo Rip, Little Rip]]\n       \n       9.5.6 [[Dynamical Forms of Dark Energy#The Statefinder|The Statefinder]]\n       \n       9.5.7 [[Dynamical Forms of Dark Energy#Crossing the Phantom Divide|Crossing the Phantom Divide]]\n       \n   9.6 [[Lost and Found|Lost and Found]]\n   \n   9.7 [[Single Scalar Cosmology|Single Scalar Cosmology]]\n\n10. [[:Category:Dark Matter|'''Dark Matter''']]\n   \n   10.1 [[Observational Evidence of the Dark matter Existence|Observational Evidence of the Dark matter Existence]]\n      \n   10.2 [[ANONIMOUS|ANONIMOUS]]\n   \n   10.3 [[Dark Matter Halo|Dark Matter Halo]]\n   \n   10.4 [[Candidates for Dark Matter Particles|Candidates for Dark Matter Particles]]\n        \n        10.4.1 [[Candidates for Dark Matter Particles#Standard Model Particles as Dark Matter Candidates|Standard Model Particles as Dark Matter Candidates]]\n        \n        10.4.2 [[Candidates for Dark Matter Particles#Supersymmetric Candidate Particles|Supersymmetric Candidate Particles]]\n   \n   10.5 [[Dark Matter Detection|Dark Matter Detection]]\n   \n   10.6 [[The Dark Matter in the Solar System|The Dark Matter in the Solar System]]\n   \n   10.7 [[The Dark Stars|The Dark Stars]]\n   \n11. [[:Category:Interactions in the Dark Sector|'''Interactions in the Dark Sector''']]\n   \n   11.1 [[Physical mechanism of energy exchange|Physical mechanism of energy exchange]]\n   \n   11.2 [[Phenomenology of interacting models|Phenomenology of interacting models]]\n   \n   11.3 [[Simple linear models|Simple linear models]]\n   \n   11.4 [[Cosmological models with a change of the direction of energy transfer|Cosmological models with a change of the direction of energy transfer]]\n           \n   11.5 [[Non-linear interaction in the dark sector|Non-linear interaction in the dark sector]]\n   \n   11.6 [[Phase space structure of models with interaction|Phase space structure of models with interaction]]\n   \n   11.7 [[Peculiarity of dynamics of scalar field coupled to dark matter|Peculiarity of dynamics of scalar field coupled to dark matter]]\n   \n        11.7.1 [[Peculiarity of dynamics of scalar field coupled to dark matter#Interacting quintessence model|Interacting quintessence model]]\n        \n        11.7.2 [[Peculiarity of dynamics of scalar field coupled to dark matter#Interacting phantom|Interacting phantom]]\n        \n   11.8 [[Realization of interaction in the dark sector|Realization of interaction in the dark sector]]\n        \n        11.8.1 [[Realization of interaction in the dark sector#Vacuum decay into cold dark matter|Vacuum decay into cold dark matter]]\n               \n        11.8.2 [[Realization of interaction in the dark sector#Time-dependent cosmological \"constant\"|Time-dependent cosmological \"constant\"]]\n               \n    11.9 [[Statefinder parameters for interacting dark energy and cold dark matter|Statefinder parameters for interacting dark energy and cold dark matter]]\n        \n    11.10 [[Interacting holographic dark energy|Interacting holographic dark energy]]\n        \n    11.11 [[Transient acceleration|Transient acceleration]]\n      \n12. [[:Category:Standard Cosmological Model|'''Standard Cosmological Model''']]\n   \n   12.1 [[Characteristic Parameters and Scales|Characteristic Parameters and Scales]]\n   \n   12.2 [[Evolution of Universe|Evolution of Universe]]\n\n13. [[:Category:Weak field limit and gravitational waves|'''Weak field limit and gravitational waves''']]\n   \n   13.1 [[Motivation and symmetries / Introduction|Motivation and symmetries / Introduction]]\n   \n   13.2 [[Linearized Einstein equations|Linearized Einstein equations]]\n   \n   13.3 [[Gauge transformations and degrees of freedom|Gauge transformations and degrees of freedom]]\n   \n   13.4 [[Wave equation|Wave equation]]\n   \n   13.5 [[Transverse traceless gauge|Transverse traceless gauge]]\n   \n   13.6 [[Gravitational waves and matter|Gravitational waves and matter]]\n   \n   13.7 [[Energy of gravitational waves|Energy of gravitational waves]]\n   \n   13.8 [[Binary systems|Binary systems]]\n   \n   13.9 [[Gravitational Waves: scale of the phenomenon|Gravitational Waves: scale of the phenomenon]]\n   \n   13.10 [[Generation and detection of gravitational waves|Generation and detection of gravitational waves]]\n\n14. [[:Category:Observational Cosmology|'''Observational cosmology''']]\n   \n   14.1 [[Point gravitational lenses|Point gravitational lenses]]\n   \n   14.2 [[Microlensing and Weak Lensing|Microlensing and weak lensing]]\n\n15. [[:Category:Holographic Universe|'''Holographic Universe''']]\n   \n   15.1 [[Information, Entropy and Holographic Screen|Information, Entropy and Holographic Screen]]\n\n16. [[:Category:Horizons|'''Horizons''']]\n   \n   16.1 [[Simple English|Simple English]]\n   \n   16.2 [[Simple Math|Simple Math]]\n   \n   16.3 [[Composite Models|Composite Models]]\n   \n   16.4 [[Causal Structure|Causal Structure]]\n   \n   16.5 [[Conformal diagrams: stationary black holes|Conformal diagrams: stationary black holes]]\n   \n        16.5.1 [[Conformal diagrams: stationary black holes#Schwarzschild-Kruskal black hole solution|Schwarzschild-Kruskal black hole solution]]\n        \n        16.5.2 [[Conformal diagrams: stationary black holes#Other spherically symmetric black holes|Other spherically symmetric black holes]]\n   \n   16.6 [[Hubble sphere|Hubble sphere]]\n   \n   16.7 [[Proper horizons|Proper horizons]]\n   \n   16.8 [[Inflation|Inflation]]\n   \n   16.9 [[Holography|Holography]]\n\n17. [[:Category:Deceleration Parameter|'''Deceleration Parameter''']]\n\n18. [[:Category:Quantum Cosmology|'''Quantum Cosmology''']]"
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