Physical Foundations of Cosmology

60 Propagation of light and horizons Note that asz→∞,χ(z)approaches the particle horizon. Hence, the redshift parameter measures ...

2.5 Kinematic tests 61 observer l χem φ 0 tem ∆θ θ 0 + ∆θ χ= 0 t=t 0 φ 0 = const θ 0 = const Fig. 2.11. tempropagate along radia ...

62 Propagation of light and horizons increases with distance and as it approaches the horizon its image covers the whole sky. Of ...

2.5 Kinematic tests 63 z ∆θ z = (^5) / 4 Fig. 2.12. directions in the sky differs; this temperature difference depends on the an ...

64 Propagation of light and horizons 2.5.2Luminosity–redshiftrelation A second method of recovering the expansion history is wit ...

2.5 Kinematic tests 65 whereq 0 ≡− ( a ̈/aH^2 ) 0 .In turn, the value of the deceleration parameterq^0 is determined by the equa ...

66 Propagation of light and horizons 1 redshift z 1.5 2 apparent magnitude m bol Ωm = 0 Ωm = 0.3 Ωm = 1 0.5 Fig. 2.13. Problem 2 ...

2.5 Kinematic tests 67 a moment of time characterized by redshiftzis spatially uniform and equal ton(z). Then, the number of gal ...

68 Propagation of light and horizons In a flat universe, where 0 =1 and (^) = 1 − (^) m, the redshift drift,v≡ z/(1+z),is eq ...

3 The hot universe In the previous chapters we studied the geometrical properties of the universe. Now we turn to its thermal hi ...

70 The hot universe black holes. We will see later that the data on light element abundances and CMB fluctuations clearly indica ...

3.1 The composition of the universe 71 zeq zQ 0 z (^) m (^) γ (^) Q Fig. 3.1. The radiation energy density grows faster than the ...

72 The hot universe Problem 3.3Dark energy with equation of statew=− 1 /3 leads to a term∝ 1 /a^2 in the Friedmann equation (1.6 ...

3.2 Brief thermal history 73 of the light elements resulting fromprimordial nucleosynthesisare in very good agree- ment with ava ...

74 The hot universe Unification scales. It is remarkable and fortunate that the most important robust predictions of inflation d ...

3.3 Rudiments of thermodynamics 75 whereλ∼ 1 /pis the de Broglie wavelength andp=E∼Tis the typical momen- tum of the colliding u ...

76 The hot universe a closed system and does not use any concepts from equilibrium thermodynamics. Therefore, it can also be app ...

3.3 Rudiments of thermodynamics 77 The total number of states for the whole system, therefore, is ({N})= ∏  G. (3.13) Subs ...

78 The hot universe μ≡λ 2 T(kB=1). The distribution function (3.19) then takes the form n= 1 exp((−μ)/T)− 1 . (3.20) This spec ...

3.3 Rudiments of thermodynamics 79 signs as a consequence of electric charge conservation. Only if the total electric charge of ...