probset6a

Probset6a - COSMOLOGY Problem Set 6 May 3 2010 Problem 1 Bosonic Neutrinos Suppose the three “standard” neutrinos ν e ν μ ν τ were Bosons

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Unformatted text preview: COSMOLOGY Problem Set 6 May 3, 2010 Problem 1 : Bosonic Neutrinos Suppose the three “standard” neutrinos ( ν e , ν μ , ν τ ) were Bosons instead of Fermions. For temperatures in the range m e ≪ T γ ≪ m μ , find: a) The new effective number of degrees of freedom g ′ eff . [5] b) The expansion rate “speed-up” factor, S ≡ H ′ /H (compared to the standard case where neutrinos are fermions). [5] c) Assume that the bosonic neutrinos decouple prior to e ± annihilation (as do the standard fermionic neutrinos). Find the ratio at present of neutrino temperature to photon temperature. [5] d) Find the expansion rate “speed-up” factor, S ≡ H ′ /H , during the post- e ± annihi- lation, radiation dominated era. [5] Problem 2 : Sterile Neutrino Suppose there is a fourth flavor of massive, but light ( m ν s ≪ m e ), neutrinos, ν s , which through mixing (oscillations) with the standard neutrinos are in equilibrium at temperatures T γ > T νdec > m e . Assume that this 4th (“sterile”) neutrino decouples....
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This note was uploaded on 07/28/2011 for the course PHY 880.20 taught by Professor Steigman during the Spring '10 term at Ohio State.

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Probset6a - COSMOLOGY Problem Set 6 May 3 2010 Problem 1 Bosonic Neutrinos Suppose the three “standard” neutrinos ν e ν μ ν τ were Bosons

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