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# ps5 - Phys/Astro 228 Extragalactic Astronomy and Cosmology...

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Phys/Astro 228: Extragalactic Astronomy and Cosmology October 13 2006 C.–P. Ma Problem Set 5 Due in class Friday October 20 Readings: (1) Ch 2.4 of Dodelson; (2) All of “Dark Matter” from Particle Physics Review (linked at course website). 1. Equality Time (a) Radiation-Matter Equality : The correct answer to Problem 2(d) of Problem Set 4 is: the present-day radiation density is Ω 0 ,r h 2 = 4 . 15 × 10 5 . From this, calculate the equality redshift, z eq , at which the energy density in matter equals that in the radiation. (Leave Ω 0 ,m and h as free variables in your answer.) Approximately how old was the universe at z eq , for a model of Ω 0 ,m = 0 . 27, Ω 0 , Λ = 0 . 73, and h = 0 . 71? (b) Matter- Λ Equality : For the same model (i.e. Ω 0 ,m = 0 . 27, Ω 0 , Λ = 0 . 73), calculate the redshift at which the energy density in matter equals that in the cosmological constant. (c) Make a simple sketch showing how the energy density in radiation, matter, and Λ evolves with the expansion factor

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ps5 - Phys/Astro 228 Extragalactic Astronomy and Cosmology...

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