a) The evolution equation for the density contrast in a non-expanding universe is given by +²²8-4Gp8 = 0, where k is the wavenumber, ² is the adiabatic sound speed and p is the matter energy density in the background. i) Read off the Jeans wave number, kj, from the evolution equation above, and give the Jeans length, AJ. Briefly discuss the meaning of the Jeans length. ii) Solve the equation above in the case of c² and p constant but non-zero. b) Assume that the evolution equation for the density contrast & is given by +D-8+ a k2 a² δ - 4Gπρδ = 0, where D is a positive constant, k is the comoving wave number, and p is the matter energy density in the background. Solve the equation above in order to find the time evolution for 8 in the case of a flat universe dominated by matter. c) Briefly describe two pieces of observational evidence for the existence of dark matter.
a) The evolution equation for the density contrast in a non-expanding universe is given by +²²8-4Gp8 = 0, where k is the wavenumber, ² is the adiabatic sound speed and p is the matter energy density in the background. i) Read off the Jeans wave number, kj, from the evolution equation above, and give the Jeans length, AJ. Briefly discuss the meaning of the Jeans length. ii) Solve the equation above in the case of c² and p constant but non-zero. b) Assume that the evolution equation for the density contrast & is given by +D-8+ a k2 a² δ - 4Gπρδ = 0, where D is a positive constant, k is the comoving wave number, and p is the matter energy density in the background. Solve the equation above in order to find the time evolution for 8 in the case of a flat universe dominated by matter. c) Briefly describe two pieces of observational evidence for the existence of dark matter.
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
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Transcribed Image Text:a) The evolution equation for the density contrast in a non-expanding universe is given by
+²²8-4Gp8 = 0,
where k is the wavenumber, ² is the adiabatic sound speed and p is the matter energy
density in the background.
i) Read off the Jeans wave number, kj, from the evolution equation above, and give the
Jeans length, AJ. Briefly discuss the meaning of the Jeans length.
ii) Solve the equation above in the case of c² and p constant but non-zero.
b) Assume that the evolution equation for the density contrast & is given by
+D-8+
a
k2
a²
δ - 4Gπρδ = 0,
where D is a positive constant, k is the comoving wave number, and p is the matter energy
density in the background.
Solve the equation above in order to find the time evolution for 8 in the case of a flat universe
dominated by matter.
c) Briefly describe two pieces of observational evidence for the existence of dark matter.
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