Cosmological solutions of the Einstein-Friedmann equations ...

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Cosmology Note: z = constant is the circle: (cT) 2 + W2 = constant. Homogeneity and Isotropy follow from the symmetry: S + 4 is invariant under S O(2, 3). The force is linear attractive F ∝ −1 3 Λ r. Causality problem: periodicity in time ct → ct + 2 π a. The circle in the (cT, W) plane is acausal. May be cured by mapping the circle to the real line: which is the universal cover of the AdS space. For the cosmological solutions of the Einstein-Friedmann equations the RW-metric is only affected as far as S (t) solves a different dynamical equation. Exercise: find the model Einstein proposed: an eternal static solution. Show that Einstein’s GRT with vanishing cosmological constant has no such solution. Exercise: the observation of planetary motions constrains the cosmological constant to |Λ| ≪ 10 −42 cm −2 !. Show that this is compatible with a dark energy density, which has been determined to be ΩΛ ∼ 0.74 ± 0.03. Previous ≪❘ , next ❘≫ lecture. c○ 2009, F. Jegerlehner ≪❘ Lect. 7 ❘≫ 486
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Cosmology Cosmological solutions of
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Cosmology Cosmological solutions of
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Cosmology claimed to represent the
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Cosmology A) Empty Worlds, vacuum e
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Cosmology A) Empty Worlds, vacuum e
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Cosmology The general solution is S
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Cosmology (d) Λ > 0 , k = 0: S = e
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Cosmology Terminology: Λ > 0 , k =
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Cosmology B) Matter dominated: ρ >
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Cosmology B) Matter dominated: ρ >
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Cosmology ct = C arcsin √ X −
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Cosmology In each case we have S (t
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Cosmology Einstein-de Sitter univer
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Cosmology Einstein-de Sitter univer
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Cosmology t = 2 3 H−1 (t) (EdS) H
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Cosmology t = 2 3 H−1 (t) (EdS) H
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Cosmology Back to the non-flat geom
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Cosmology Back to the non-flat geom
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Cosmology in terms of the observabl
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Cosmology The conclusion of the abo
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Cosmology C) Radiation dominated: p
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Cosmology ❖ k = 0 : S (t) = 4 ¯
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Cosmology κ ρ(t) = 3 H2 (t) K(t)
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Cosmology Actually, in the radiatio
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Cosmology Actually, in the radiatio
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Cosmology 8π hν ργ(ν) dν = 3
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Cosmology 8π hν ργ(ν) dν = 3
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Cosmology Since ρ(t)S (t) 4 = ρ0S
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Cosmology c○ 2009, F. Jegerlehner
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Cosmology and Dicke and Peebles at
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Cosmology T0 = (2.725 ± 0.002) ◦
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Cosmology T0 = (2.725 ± 0.002) ◦
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Cosmology However, the evolution of
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Cosmology However, the evolution of
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Cosmology ρ(t) Big Bang radiation
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Cosmology The critical energy densi
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Page 121 and 122: Cosmology Ω0 = 1 c○ 2009, F. Je
Page 123 and 124: Cosmology Ω0 = 1 is the critical
Page 129 and 130: Cosmology ˙S 2 c 2 + k = κ 3 ρ S
Page 131 and 132: Cosmology ˙S 2 c 2 + k = κ 3 ρ S
Page 133 and 134: Cosmology q0 = κ (ρ0+3 p0) 6 H 2
Page 135 and 136: Cosmology Form of energy equation o
Page 141 and 142: Cosmology in which case, independen
Page 147 and 148: Cosmology (in accord with the unive
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Page 151 and 152: Cosmology missing part making Ω =
Page 153 and 154: Cosmology missing part making Ω =
Page 155 and 156: Cosmology Appendix: Λ 0 The issue
Page 157 and 158: Cosmology physical effect of a non-
Page 159 and 160: Cosmology and the metric ds 2 = 1
Page 161 and 162: Cosmology and the metric ds 2 = 1
Page 163 and 164: Cosmology With a 2 1 K = 3 Λ ; a
Page 165 and 166: Cosmology With a 2 1 K = 3 Λ ; a
Page 167 and 168: Cosmology Λ < 0: Anti-de Sitter sp
Page 169 and 170: Cosmology Λ < 0: Anti-de Sitter sp
Page 171: Cosmology Note: z = constant is the
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