Cosmological solutions of the Einstein-Friedmann equations ...

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Cosmology Ω0 = 1 is the critical density for which the universe just remains open, infinite and flat. Ω0 > 1 the case of much matter, space closes due to gravitational attraction of mass. Gravity stops the expansion after finite time, the universe collapses, ends in heat death! Ω0 < 1 the case of little matter, gravity not sufficient to stop expansion, universe expands forever, space open, ends in freezing to death! c○ 2009, F. Jegerlehner ≪❘ Lect. 7 ❘≫ 471
Cosmology Ω0 = 1 is the critical density for which the universe just remains open, infinite and flat. Ω0 > 1 the case of much matter, space closes due to gravitational attraction of mass. Gravity stops the expansion after finite time, the universe collapses, ends in heat death! Ω0 < 1 the case of little matter, gravity not sufficient to stop expansion, universe expands forever, space open, ends in freezing to death! If we include the cosmological constant as a vacuum energy density in the total density ρ, we may write the Friedmann equations in the form c○ 2009, F. Jegerlehner ≪❘ Lect. 7 ❘≫ 471
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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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Page 75 and 76: Cosmology C) Radiation dominated: p
Page 81 and 82: Cosmology ❖ k = 0 : S (t) = 4 ¯
Page 83 and 84: Cosmology In each case we have S (t
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 125: 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
Page 149 and 150: Cosmology (in accord with the unive
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 and 172: Cosmology Note: z = constant is the
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