Introduction to Cosmology

5 Cosmological Models In Section 5.1 we turn to the ‘concordance’ or Friedmann–Lemaitre–Robertson– Walker (FLRW) model of cosmol ...

82 Cosmological Models component푇 00 and the space–space component푇 11 are then 푇 00 =휌푐^2 ,푇 11 = 푝푎^2 1 −푘휎^2 , (5.1) taking푔 ...

Friedmann–Lemaitre Cosmologies 83 At our present time푡 0 when the mass density is휌 0 , the cosmic scale is 1, the Hub- ble param ...

84 Cosmological Models Einstein Universe. Consider now the static universe cherished by Einstein. This is defined by푎(푡)being co ...

Friedmann–Lemaitre Cosmologies 85 right-hand side, where they appear as corrections to the stress–energy tensor푇휇휈.Then the phys ...

86 Cosmological Models This equation does not contain푘and휆, but that is not a consequence of having started from Equations (5.4) ...

Friedmann–Lemaitre Cosmologies 87 of light, but freely propagating light did not exist at times when푧≳1080, so푧is then no longer ...

88 Cosmological Models In fact, this inequality is always true when 푘=+ 1 ,푝>−^1 3 휌푐^2 ,푤>−^1 3 ,휆> 0. (5.36) Then we ...

Friedmann–Lemaitre Cosmologies 89 and (5.18) that the Universe has always decelerated. It then follows that푎must have been zero ...

90 Cosmological Models Then푡maxis obtained by integrating푡from 0 to푡maxand푎from 0 tomax, 푡max=^1 푐∫ 푎max 0 d푎 ( 8 휋퐺 3 푐^2 휌m(푎) ...

Friedmann–Lemaitre Cosmologies 91 R(t) de Sitter H constant k = – 1 k = 0 future 0 1 + 1 tmax t tH to past k = (^23) tH Figure ...

92 Cosmological Models Let us now return to the general expression [Equation (5.14)] for the normalized age푡(푧)∕푡 0 or푡(푎)∕푡 0 o ...

de Sitter Cosmology 93 5.2 de Sitter Cosmology Let us now turn to another special case for which the Einstein equation can be so ...

94 Cosmological Models Although the world is not devoid of matter and the cosmological constant is small, the de Sitter universe ...

The Schwarzschild Model 95 The importance of the de Sitter model will be illustrated later when we deal with exponential expansi ...

96 Cosmological Models The larger the ratio푀∕푟of the star, the higher is the required escape velocity. Ultimately, in the ultra- ...

Black Holes 97 of the emitted photons is unchanged푐their frequency휈goes to zero, and the energy 퐸=ℎ휈of the signal vanishes. One ...

98 Cosmological Models D C E 0 B A Spacecraft world line Observer world line tE tmax rc rs ro to tA t t Figure 5.3The world li ...

Black Holes 99 An interesting quantity is the Schwarzschild radius of the Universe,푟c,U. Combining Equations (5.50) and (5.70) w ...

100 Cosmological Models However, there may be reasons to doubt the properties of classical event horizons. The Schwarzschild met ...