Deriving the second Friedman equation from the first.

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SUMMARY

The discussion centers on the relationship between the first and second Friedman equations in cosmology. It is established that the first Friedman equation, when combined with its time derivative and the continuity equation, can indeed imply the second Friedman equation. The continuity equation, which ensures the divergence-free nature of the stress-energy tensor, is crucial for this derivation. Participants confirm the validity of the professor's statement regarding the algebraic implications of these equations.

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  • Understanding of the Friedman equations in cosmology
  • Knowledge of the continuity equation in general relativity
  • Familiarity with stress-energy tensors
  • Basic algebraic manipulation skills in physics
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  • Study the derivation of the first Friedman equation
  • Explore the implications of the continuity equation in cosmology
  • Learn about stress-energy tensors and their role in general relativity
  • Investigate the mathematical techniques for deriving equations in cosmological models
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Students of cosmology, physicists interested in general relativity, and anyone seeking to deepen their understanding of the Friedman equations and their implications in cosmological models.

thebiggerbang
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Hello!

My professors asked me why we don't usually consider the second Friedman equation. He told me that the solutions for the first always give a solution for the second. He told me that the first equation along with it's time derivative can imply the second equation. I have been trying the algebra for a long time now, but I am not being able to get ahead.

I wanted to know if the statement that the professor made is true in the first place.
 
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You cannot just take the time derivative. You will also need to apply the continuity equation (i.e., the fact that the stress-energy tensor is divergence free).
 
Thank you, that helped!
 

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