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E. 106) CHAPTER 2. 1 1 r/rs 10 Singular and non-singular isothermal and NFW density and mass profiles 62 CHAPTER 2. g. its mass • it is currently unclear how the density profile arises; also, its slope near the core is being discussed Chapter 3 The Early Universe 63 CHAPTER 3. e.

E. 29) that density perturbations grow ∝ a2 during the radiation-dominated era, and ∝ a afterwards • as the universe expands, the Hubble radius grows, and thus the scale of perturbations which can be in causal contact; a density perturbation mode is said to “enter the horizon” when its wave length λ equals the Hubble radius • modes entering the horizon while radiation dominates feel the radiation pressure, which almost completely stops the growth of the density perturbation until matter starts dominating and radiation pressure quickly becomes negligible; accordingly, modes which are small enough to enter the horizon before aeq are relatively suppressed compared to larger modes which enter the horizon afterwards 47 CHAPTER 2.

E. 78) CHAPTER 2. 84) ∆v 150 this means that a halo can be considered collapsed when its density contrast expected from linear theory has reached the value of δc ; this value depends very little on the cosmological parameters, so it can be quite generally used although it was derived for the Einstein-de Sitter model 140 130 120 ΛCDM OCDM Ω=1 QCDM, w=-2/3 QCDM, w=-1/3 110 100 0 1 2 3 collapse redshift 4 5 virial overdensity in different cosmologies as a function of the halo collapse redshift 55 CHAPTER 2.

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Cosmology by Bartelmann M.

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