What Is the Age of the Universe According to Different Models of Cosmology?

In summary, this conversation discusses the total density of the Universe and the role of dark energy, as well as two mathematical models with different values for Omega_matter and Omega_lambda. The expansion scale and age of the Universe are calculated for both models, and it is noted that a matter-dominated universe would be too young. The conversation ends with a question about whether the data on the oldest Globular clusters supports one model over the other.
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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.
 
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  • #2
I'm also not sure if the equation for a''(t) is the equation of motion for a matter-dominated universe.
 

1. What is the scale factor in cosmology?

The scale factor in cosmology is a measure of the relative size of the universe at a given time compared to its size at a reference time. It is used to describe the expansion of the universe and is typically denoted by the symbol "a".

2. How does the scale factor change over time?

The scale factor changes over time as the universe expands. In the early stages of the universe, the scale factor was much smaller, indicating a smaller size of the universe. As time progresses, the scale factor increases, signifying the expansion of the universe.

3. What is the relationship between the scale factor and the age of the universe?

The scale factor and the age of the universe are directly related. The age of the universe is equal to the reciprocal of the Hubble constant, which is a measure of the expansion rate of the universe. Therefore, as the scale factor increases, the age of the universe also increases.

4. How is the scale factor measured?

The scale factor is measured through various cosmological observations, such as the redshift of distant galaxies and the cosmic microwave background radiation. These observations provide information about the expansion of the universe, which can then be used to calculate the scale factor.

5. Can the scale factor change over time?

Yes, the scale factor can change over time. In fact, it has been observed that the expansion of the universe is accelerating, which means that the scale factor is increasing at an increasingly faster rate. This is attributed to the presence of dark energy, which is a mysterious force that is causing the expansion of the universe to accelerate.

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