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probset7a - COSMOLOGY Problem Set 7 Problem 1 Another...

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COSMOLOGY Problem Set 7 May 10, 2010 Problem 1 : Another Sterile Neutrino Suppose there is a new, very weakly interacting, “sterile” neutrino ν s which does not mix with the usual (“active”) neutrinos. The ν s are light but not massless (0 negationslash = m ν s 1 MeV). a) If these sterile neutrinos decouple at a temperature of 10 GeV, find their contribu- tion to ΔN ν ρ ν s ν , the effective number of equivalent neutrinos at T γ 1 MeV. [10] b) Assume that these ν s are non-relativistic at present. In terms of their mass m ν s , find the present value of their density parameter Ω ν s 0 . (You may adopt H 0 = 70 km/s/Mpc and T γ 0 = 2 . 725 K). If observations require that the upper bound to their present density is Ω ν s 0 0 . 23, find the upper bound to the ν s mass. [10] Problem 2 : Early Universe Neutron – Proton Ratio In the early Universe the charged-current weak interactions keep neutrons and protons in equilibrium (“chemical” equilibrium) until (approximately) the weak rate (Γ wk )
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