Cosmological solutions of the Einstein-Friedmann equations ...

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Cosmology (d) Λ > 0 , k = 0: S = exp ct c a = exp (Ht) ; H ≡ a = κ ρvac c2 /3 de Sitter Universe: here H(t) = constant and q(t) ≡ −1, this universe has infinite age! Today’s pure dark energy universe! (e) Λ > 0 , k = −1: S = a sinh ct a . (f) Λ < 0 , k = −1: S = a sin ct a . where in all cases a = |3/Λ| . c○ 2009, F. Jegerlehner ≪❘ Lect. 7 ❘≫ 443
Cosmology (d) Λ > 0 , k = 0: S = exp ct c a = exp (Ht) ; H ≡ a = κ ρvac c2 /3 de Sitter Universe: here H(t) = constant and q(t) ≡ −1, this universe has infinite age! Today’s pure dark energy universe! (e) Λ > 0 , k = −1: S = a sinh ct a . (f) Λ < 0 , k = −1: S = a sin ct a . where in all cases a = |3/Λ| . Models (b), (d), (e) and (f) some times have been called “incomplete” as <strong>the</strong>y exhibit more space than “substrate”. c○ 2009, F. Jegerlehner ≪❘ Lect. 7 ❘≫ 443
Page 1 and 2: Cosmology Cosmological solutions of
Page 3 and 4: Cosmology Cosmological solutions of
Page 5 and 6: Cosmology claimed to represent the
Page 11 and 12: Cosmology A) Empty Worlds, vacuum e
Page 13 and 14: Cosmology A) Empty Worlds, vacuum e
Page 15 and 16: Cosmology The general solution is S
Page 21 and 22: Cosmology (d) Λ > 0 , k = 0: S = e
Page 23: Cosmology (d) Λ > 0 , k = 0: S = e
Page 27 and 28: 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
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Cosmology C) Radiation dominated: p
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Cosmology ❖ k = 0 : S (t) = 4 ¯
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Cosmology In each case we have S (t
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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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Cosmology Ω0 = 1 c○ 2009, F. Je
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Cosmology Ω0 = 1 is the critical
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Cosmology ˙S 2 c 2 + k = κ 3 ρ S
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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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