This book presents a high-level study of cosmology with interacting dark energy and no additional fields. It is known that dark energy is not necessarily uniform when other sources of gravity are present: interaction with matter leads to its variation in space and time. The present text studies the cosmological implications of this circumstance by analyzing cosmological models in which the dark energy density interacts with matter and thus changes with the time. The book also includes a translation of a seminal article about the remarkable life and work of E.B. Gliner, the first person to suggest the concept of dark energy in 1965.
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1 Introduction. Non-uniform Dark Energy |
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1 | (4) |
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3 | (2) |
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2 Friedmann Cosmology with Changing Dark Energy |
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5 | (4) |
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3 Cosmology with Dark Energy and a Single Type of Matter: General Interaction Model |
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9 | (30) |
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3.1 Linear Interaction Between Dark Energy and Matter. Exact Solution for Singular Cosmology Dominated by Dark Energy |
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12 | (3) |
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3.2 The Role of Non-linearity: Interaction Laws F(pvac, p) = f(p) and the Corresponding Class of Exact Solutions |
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15 | (5) |
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3.2.1 General Solution and Its Properties |
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15 | (2) |
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3.2.2 Example: Exact Solution for a Special Form of Function f(p) |
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17 | (3) |
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3.3 Non-singular Cosmological Solutions Starting and Ending with Pure Dark Energy (de Sitter Universe) |
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20 | (9) |
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3.3.1 A Toy Linear Model: Initial Jump in the Density |
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21 | (3) |
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3.3.2 General Non-linear Model: Qualitative Picture. Non-singular Cosmologies Represented by Heteroclynic Phase Trajectories |
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24 | (5) |
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3.4 Non-singular Cosmologies: Exact Solutions |
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29 | (10) |
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3.4.1 General Exact Solution by the Semi-inverse Method |
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29 | (4) |
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3.4.2 Particular Non-singular Cosmologies: Examples of Exact Solutions |
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33 | (4) |
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37 | (2) |
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4 Friedmann Cosmology with Interaction Between Dark Energy and Multi-Phase Matter |
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39 | (18) |
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4.1 Single Matter Phase Interacting with Dark Energy |
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40 | (1) |
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4.2 Any Number of Matter Phases Interacting with Dark Energy |
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41 | (12) |
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4.2.1 Linear Interaction Laws |
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43 | (3) |
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4.2.2 Quadratic Interaction Laws |
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46 | (4) |
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4.2.3 Non-singular Cosmologies |
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50 | (3) |
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4.3 Three Matter Phases: A Model for Our Universe |
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53 | (4) |
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55 | (2) |
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57 | (2) |
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58 | (1) |
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6 Why Does the Universe Expand? (A Tribute to E.B. Gliner) |
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59 | (12) |
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6.1 Inflation, or Blow-Up |
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59 | (2) |
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61 | (4) |
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6.3 V.L. Ginzburg: We Owe Gliner |
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65 | (1) |
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6.4 Einstein-Gliner Vacuum |
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66 | (5) |
| Appendix A The pvac(H) Model as a Particular Case of the Model (3.4) |
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71 | (4) |
| Appendix B Two Classes of Non-linear Interaction Laws Allowing for General Explicit Solutions (the Case of a Single Matter Phase) |
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75 | (2) |
| Appendix C Behavior of Non-singular Cosmological Solutions Obtained by the Semi-Inverse Method in the Beginning and at the End of the Expansion (the Case of a Single Matter Phase) |
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77 | |
Alex Silbergleit is senior research scientist at Stanford University and member of the scientific team behind NASA/Stanfords Gravity Probe B experiment that successfully confirmed Einsteins prediction of frame-dragging by the Earths gravitomagnetic field. His work is in mathematical and theoretical physics, on which he has authored over 160 papers and two books. He also translates from Russian. His official biography can be found in Whos Who In America.
Arthur D. Chernin is professor at the Sternberg Astronomical Institute, Moscow University. His work involves various aspects of theoretical physics and cosmology, fields in which he has authored over 250 papers and 10 books including Alexander A. Friedmann: The man who made the Universe expand (with E.A. Tropp, V.Ya. Frenkel) Cambrige Univ. Press, 1993, 260 pp. and Paths to dark energy (with G.G. Byrd, M.J. Valtonen, P. Teerikorpi). De Gryuter, Boston/Berlin, 2012, 400 pp.
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