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gChinkin
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Homework Statement
From CMB measurements, we know the total density of the Universe matches the critical density to 2 percent. From observations of Supernova it seems that 70 percent of that is in the form of dark energy. But the supernova observations are not as solid as the CMB result. Maybe they are in error. In this problem you will compare two mathematical models of the universe, the first with Omega_matter = 1, Omega_lambda = 0, and the second with Omega_matter = 0.3, Omega_lambda = 0.7. In both models we will have the same Hubble parameter today, Ho = 72 km/s Mpc.
Calculate numerically the history of the expansion scale a(t) in the two cases. Make a plots of a(t), in which there is a particular time (right now) where each of the curves have the same value of a and slope da/dt
Determine the age of the expansion for the two cases. Which is the older universe and by how much?
The oldest Globular clusters is 13 Gy old. Does that data support one model over the other?
Homework Equations
OmegaLambda= [tex]\Lambda[/tex]c2 /(3 (Ho)2 )
ForceLambda = ([tex]\Lambda[/tex]mc2)r(t)/3
Where r(t) is the distance from the origin or some central point I think
a''(t) = −k/a(t)2
The Attempt at a Solution
I honestly have no idea. After looking around the internet for a few hours, I can't even verify that these equations (which my professor told me to use) are correct.
A matter dominated universe should lead to a universe too young, but I'm not sure why.