Cosmological solutions of the Einstein-Friedmann equations ...

More documents

Recommendations

Info

$Einführung in LaTeX - Www-com.physik.hu-berlin.de$

Cosmology q0 = κ (ρ0+3 p0) 6 H 2 0 = ρ0+3 p0 2 ρ 0,crit This equation provides a simple explanation for the different values q0 takes depending on the form of the equation of state: c○ 2009, F. Jegerlehner ≪❘ Lect. 7 ❘≫ 473
Cosmology Form of energy equation of state q0 q0(k = 0) a) vacuum energy: pΛ = −ρΛ q0 = −ΩΛ q0 = −1, b) non-relativistic matter: pmat = 0 q0 = 1 2 Ωmat q0 = 1 2 , c) relativistic matter, radiation: prad = ρrad/3 q0 = Ωrad q0 = 1, the different forms of matter contribute with different signs and weights to q0. c○ 2009, F. Jegerlehner ≪❘ Lect. 7 ❘≫ 474 i.e.
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 7 and 8:
Page 9 and 10:
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 17 and 18:
Page 19 and 20:
Page 21 and 22:
Cosmology (d) Λ > 0 , k = 0: S = e
Page 23 and 24:
Page 25 and 26:
Page 27 and 28:
Cosmology Terminology: Λ > 0 , k =
Page 29 and 30:
Page 31 and 32:
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 39 and 40:
Page 41 and 42:
Page 43 and 44:
Cosmology In each case we have S (t
Page 45 and 46:
Page 47 and 48:
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 63 and 64:
Page 65 and 66:
Page 67 and 68:
Page 69 and 70:
Cosmology The conclusion of the abo
Page 71 and 72:
Page 73 and 74:
Page 75 and 76:
Cosmology C) Radiation dominated: p
Page 77 and 78:
Page 79 and 80:
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 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: Cosmology q0 = κ (ρ0+3 p0) 6 H 2
Page 137 and 138: Cosmology Form of energy equation o
Page 139 and 140: 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
show all

Cosmological solutions of the Einstein-Friedmann equations ...

Create successful ePaper yourself

Delete template?

Save as template?