Cosmological solutions of the Einstein-Friedmann equations ...

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Cosmology ❖ k = 0 : S (t) = 4 ¯C 1/4 ❖ k = 1 : S (t) = (ct) 1/2 ¯C − √ ¯C − ct 2 1/2 in 0 < ct < 2 √ ¯C with cyclic extension ! ❖ k = −1 : S (t) = √ ¯C + ct 2 1/2 − ¯C c○ 2009, F. Jegerlehner ≪❘ Lect. 7 ❘≫ 458
Cosmology In each case we have S (t) → 0 (t → 0) i.e., all <strong>of</strong> <strong>the</strong>m are Big-Bang cosmologies. c○ 2009, F. Jegerlehner ≪❘ Lect. 7 ❘≫ 459
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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 Terminology: Λ > 0 , k =
Page 31 and 32: Cosmology Terminology: Λ > 0 , k =
Page 33 and 34: Cosmology B) Matter dominated: ρ >
Page 35 and 36: Cosmology B) Matter dominated: ρ >
Page 37 and 38: Cosmology ct = C arcsin √ X −
Page 43 and 44: Cosmology In each case we have S (t
Page 49 and 50: Cosmology Einstein-de Sitter univer
Page 51 and 52: Cosmology Einstein-de Sitter univer
Page 53 and 54: Cosmology t = 2 3 H−1 (t) (EdS) H
Page 55 and 56: Cosmology t = 2 3 H−1 (t) (EdS) H
Page 57 and 58: Cosmology Back to the non-flat geom
Page 59 and 60: Cosmology Back to the non-flat geom
Page 61 and 62: Cosmology in terms of the observabl
Page 69 and 70: Cosmology The conclusion of the abo
Page 75 and 76: Cosmology C) Radiation dominated: p
Page 81: Cosmology ❖ k = 0 : S (t) = 4 ¯
Page 89 and 90: Cosmology κ ρ(t) = 3 H2 (t) K(t)
Page 91 and 92: Cosmology Actually, in the radiatio
Page 93 and 94: Cosmology Actually, in the radiatio
Page 95 and 96: Cosmology 8π hν ργ(ν) dν = 3
Page 97 and 98: Cosmology 8π hν ργ(ν) dν = 3
Page 99 and 100: Cosmology Since ρ(t)S (t) 4 = ρ0S
Page 101 and 102: Cosmology c○ 2009, F. Jegerlehner
Page 103 and 104: Cosmology and Dicke and Peebles at
Page 105 and 106: Cosmology T0 = (2.725 ± 0.002) ◦
Page 107 and 108: Cosmology T0 = (2.725 ± 0.002) ◦
Page 109 and 110: Cosmology However, the evolution of
Page 111 and 112: Cosmology However, the evolution of
Page 113 and 114: Cosmology ρ(t) Big Bang radiation
Page 115 and 116: Cosmology The critical energy densi
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
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Cosmology q0 = κ (ρ0+3 p0) 6 H 2
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Cosmology Form of energy equation o
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Cosmology in which case, independen
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Cosmology (in accord with the unive
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Cosmology (in accord with the unive
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Cosmology missing part making Ω =
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Cosmology missing part making Ω =
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Cosmology Appendix: Λ 0 The issue
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Cosmology physical effect of a non-
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Cosmology and the metric ds 2 = 1
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Cosmology and the metric ds 2 = 1
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Cosmology With a 2 1 K = 3 Λ ; a
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Cosmology With a 2 1 K = 3 Λ ; a
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Cosmology Λ < 0: Anti-de Sitter sp
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Cosmology Λ < 0: Anti-de Sitter sp
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Cosmology Note: z = constant is the
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