Cosmological solutions of the Einstein-Friedmann equations ...

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Cosmology (in accord with the universal behavior just mentioned before): i.e. ˙S 2 ¯C → c2 S 2 or ˙S 2 S 2 → c2 ¯C S 4 = c2 κρ 3 ρ(t) = ρEdS(t) = 3 κ H 2 (t) c 2 . In fact the observed energy density at present is close to the critical one. This we will discuss later. Even if one counts the normal baryonic matter only one is not much more than a factor of 10 off from the critical value Ω = 1 (atoms ∼ 4%) . The c○ 2009, F. Jegerlehner ≪❘ Lect. 7 ❘≫ 476
Cosmology (in accord with the universal behavior just mentioned before): i.e. ˙S 2 ¯C → c2 S 2 or ˙S 2 S 2 → c2 ¯C S 4 = c2 κρ 3 ρ(t) = ρEdS(t) = 3 κ H 2 (t) c 2 . It is truly remarkable that at that early times, precisely when we would expect curvature the be most important, the evolution automatically picks the flat solution. This does not mean, however, that at later times when the other energy density components come in to play and even dominate the scene we have to expect a flat space one. In fact the observed energy density at present is close to the critical one. This we will discuss later. Even if one counts the normal baryonic matter only one is not much more than a factor of 10 off from the critical value Ω = 1 (atoms ∼ 4%) . The c○ 2009, F. Jegerlehner ≪❘ Lect. 7 ❘≫ 476
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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
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
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: 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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