Examining Matter Dominance in FRW Universe: Solution

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SUMMARY

The discussion focuses on the examination of matter dominance in a Friedmann-Robertson-Walker (FRW) universe, specifically using the metric ds² = -c² dt² + (t/t*)(dx² + dy² + dz²). The participants conclude that the universe is radiation dominant, as evidenced by the relationship H² ∝ 1/a⁴, which contrasts with matter dominance that would follow H² ∝ 1/a³. The FRW equation is essential for deriving these relationships.

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  • Understanding of Friedmann-Robertson-Walker (FRW) metric
  • Knowledge of cosmological parameters and their dependencies
  • Familiarity with the concepts of matter and radiation dominance in cosmology
  • Basic grasp of the Hubble parameter and its significance in cosmological models
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  • Study the Friedmann equations in detail to understand their implications for different cosmological models
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  • Explore the derivation of the Hubble parameter in various cosmological contexts
  • Investigate the role of constants like t* in cosmological metrics and their physical significance
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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

Homework Equations





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
 
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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.
 

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