a) Briefly explain the term "gravitational instability". b) Assume that the evolution equation for the density contrast & is given by k2 8+2=8+ a 28-3p6 = 0, (1) a where a and 3 are positive constants, k is the comoving wave number, and p is the matter energy density in the background.
a) Briefly explain the term "gravitational instability". b) Assume that the evolution equation for the density contrast & is given by k2 8+2=8+ a 28-3p6 = 0, (1) a where a and 3 are positive constants, k is the comoving wave number, and p is the matter energy density in the background.
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Transcribed Image Text:a) Briefly explain the term "gravitational instability".
b) Assume that the evolution equation for the density contrast & is given by
k²
x-28 - Bps = 0,
(1)
where a and 3 are positive constants, k is the comoving wave number, and p is the matter
energy density in the background.
+2²
+298 +
i) Show that in the large scale limit k = 0, equation (1) can be written as
à
5+2=8+0H²Nmd = 0, (2)
a
where is a constant and is the density parameter for matter. Determine 0.
ii) Solve Equ. (2) in order to find the time evolution for 8 in the case of a flat universe
dominated by radiation, neglecting the term containing m.
c) State the difference between Hot and Cold Dark Matter. Briefly explain why Cold Dark
Matter is needed in structure formation.
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