COSMOLOGYProblem Set 7May 10, 2010Problem 1: Another Sterile NeutrinoSuppose there is a new, very weakly interacting, “sterile” neutrinoνswhich doesnotmix with the usual (“active”) neutrinos.Theνsare light but not massless(0negationslash=mνs≪1 MeV).a) If these sterile neutrinos decouple at a temperature of 10 GeV, find their contribu-tion to ΔNν≡ρνs/ρν, the effective number of equivalent neutrinos atTγ≈1 MeV.b) Assume that theseνsare non-relativistic at present. In terms of their massmνs, findthe present value of their density parameter Ωνs0. (You may adoptH0= 70 km/s/MpcandTγ0= 2.725 K). If observations require that the upper bound to their presentdensity is Ωνs0≤0.23, find the upper bound to theνsmass. Problem 2: Early Universe Neutron – Proton RatioIn the early Universe the charged-current weak interactions keep neutrons and protonsin equilibrium (“chemical” equilibrium) until (approximately) the weak rate (Γwk)
This is the end of the preview.
access the rest of the document.