Assume that the evolution equation for the density contrast δ is given by (found in image 1 below) where α and β are positive constants, k is the comoving wave number, and ρ¯ is the matter energy density in the background. i) Show that in the large scale limit k = 0, equation (1) can be written as where θ is a constant and Ωm is the density parameter for matter. Determine θ. ii)Solve Equ. (2) in order to find the time evolution for δ in the case of a flat universe dominated by radiation, neglecting the term containing Ωm.
Assume that the evolution equation for the density contrast δ is given by (found in image 1 below) where α and β are positive constants, k is the comoving wave number, and ρ¯ is the matter energy density in the background. i) Show that in the large scale limit k = 0, equation (1) can be written as where θ is a constant and Ωm is the density parameter for matter. Determine θ. ii)Solve Equ. (2) in order to find the time evolution for δ in the case of a flat universe dominated by radiation, neglecting the term containing Ωm.
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Assume that the evolution equation for the density contrast δ is given by (found in image 1 below)
where α and β are positive constants, k is the comoving wave number, and ρ¯ is the matter
energy density in the background.
i) Show that in the large scale limit k = 0, equation (1) can be written as
where θ is a constant and Ωm is the density parameter for matter. Determine θ.
ii)Solve Equ. (2) in order to find the time evolution for δ in the case of a flat universe
dominated by radiation, neglecting the term containing Ωm.
Transcribed Image Text:2
8+26+ 0-6 – 86 = 0,
-
5+2=
(1)
Transcribed Image Text:5+2 6+0H²m6= 0,
a
(2)
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