Cosmology by Bartelmann M.

By Bartelmann M.

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G. 4 MeV is the mass difference between neutrons and protons Detailed calculation of and Gaussian fit to the last-scattering probability distribution as a function of redshift. CHAPTER 1. e. 155) CHAPTER 1. g. in stars) during cosmic history; objects need to be found which either retain the primordial element mix, or in which abundance changes can be constrained: – 2 H is observed in neutral hydrogen gas via resonant UV absorption from the ground state, or via the hyperfine transition of the ground state, or via 2 H-H molecule lines – 3 He+ is observed via the hyperfine transition of the ground state – 4 He is probed by optical recombination line emission in ionised hydrogen (HII-regions) – 7 Li is observed in the spectra of cool, low-mass stars in the Galactic halo (very old, local stellar population) heavy elements are formed by stars as early as z ∼ 6, so observations need to concentrate on gas with lowest metal abundance; possibly observed dependence of light-element abundances on metal abundance may allow extrapolation to zero enrichment • it is assumed that evolutionary corrections for 2 H, 4 He and 7 Li are low or negligible, but highly uncertain for 3 He because of later production in pre-main sequence stars and destruction in stellar interiours Lithium abundance as a function of η 37 CHAPTER 1.

G. 4 MeV is the mass difference between neutrons and protons Detailed calculation of and Gaussian fit to the last-scattering probability distribution as a function of redshift. CHAPTER 1. e. 155) CHAPTER 1. g. in stars) during cosmic history; objects need to be found which either retain the primordial element mix, or in which abundance changes can be constrained: – 2 H is observed in neutral hydrogen gas via resonant UV absorption from the ground state, or via the hyperfine transition of the ground state, or via 2 H-H molecule lines – 3 He+ is observed via the hyperfine transition of the ground state – 4 He is probed by optical recombination line emission in ionised hydrogen (HII-regions) – 7 Li is observed in the spectra of cool, low-mass stars in the Galactic halo (very old, local stellar population) heavy elements are formed by stars as early as z ∼ 6, so observations need to concentrate on gas with lowest metal abundance; possibly observed dependence of light-element abundances on metal abundance may allow extrapolation to zero enrichment • it is assumed that evolutionary corrections for 2 H, 4 He and 7 Li are low or negligible, but highly uncertain for 3 He because of later production in pre-main sequence stars and destruction in stellar interiours Lithium abundance as a function of η 37 CHAPTER 1.

E. 13) 41 CHAPTER 2. 19) CHAPTER 2. g. 27) 43 CHAPTER 2. 9 0 2 4 6 8 10 redshift z linear growth factor D+ /a as a function of redshift for different cosmologies CHAPTER 2. 39) additional solutions are possible which are vorticity-free, ∇ · u = 0; since δ can either grow or decay, δ˙ = 0, and ∇ · u = 0 can occur only where δ = 0 CHAPTER 2. g. 44) (2π)3 ky ξ(y) = CHAPTER 2. 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.

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