# Examining Matter Dominance in FRW Universe: Solution

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In summary, the FRW Universe is a mathematical model used to describe the expansion of the universe based on the Friedmann-Lemaître-Robertson-Walker metric and Einstein's field equations. Matter dominance refers to a period where matter is the dominant factor in shaping the expansion of the universe. This is determined by comparing the energy density of matter to radiation and has important implications for understanding the universe's evolution and structure.
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## Homework Statement

Metric: ds^2 = -c^2 dt^2 + (t/t*) (dx^2 + dy^2 + dz^2)

(I guess t* is a constant?)

Is this universe matter dominant? Explain

## The Attempt at a Solution

I guess you have to use the FRW equation?

Assuming the usual FRW form, we set a^2 = t/t*

to find H^2 depends on 1/a^4. This means it's radiation dominant, right?

Thanks

If H^2 depends on 1/a^4 then yes, this is radiation dominant since matter is a^-3 dependent. I didn't check the work though.

## 1. What is the FRW Universe?

The FRW Universe is a mathematical model used to describe the expansion of the universe. It is based on the Friedmann-Lemaître-Robertson-Walker metric and is a solution to Einstein's field equations in general relativity.

## 2. What is matter dominance in the FRW Universe?

Matter dominance refers to a period in the evolution of the universe where the energy density of matter is significantly higher than the energy density of radiation. This results in matter being the dominant factor in shaping the expansion of the universe.

## 3. How is matter dominance determined in the FRW Universe?

Matter dominance is determined by comparing the energy density of matter to the energy density of radiation. This can be calculated using the equations of state for matter and radiation, as well as the scale factor and redshift of the universe.

## 4. What is the significance of examining matter dominance in the FRW Universe?

Studying matter dominance in the FRW Universe allows scientists to understand the different stages of the universe's evolution and how matter has played a role in shaping it. It also provides insights into the distribution of matter and the overall structure of the universe.

## 5. What are the implications of matter dominance in the FRW Universe for our understanding of the universe?

The presence of matter dominance in the FRW Universe has important implications for our understanding of the universe. It helps us to better understand the behavior of matter and radiation during different stages of the universe's evolution, and how they have influenced the expansion and structure of the universe.

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