Friedman equations from flat FRW universe line element

Click For Summary
SUMMARY

The discussion focuses on deriving the Friedmann equations from the flat Friedmann-Robertson-Walker (FRW) universe line element. The key steps involve calculating the Christoffel symbols for the FRW metric and using the 0-0 component of the Einstein Field Equations. Specifically, the equation R_{00} - (1/2) g_{00} R must be equated to the zeroth component of the stress-energy momentum tensor multiplied by 8πG. Participants also seek recommendations for relevant literature to aid in this calculation.

PREREQUISITES
  • Understanding of Einstein Field Equations
  • Familiarity with the Friedmann-Robertson-Walker (FRW) metric
  • Knowledge of Christoffel symbols and their calculation
  • Basic concepts of stress-energy momentum tensor
NEXT STEPS
  • Study the derivation of the Friedmann equations from the FRW metric
  • Learn about calculating Christoffel symbols in general relativity
  • Explore the implications of the stress-energy momentum tensor in cosmology
  • Read "Cosmology" by Steven Weinberg for in-depth understanding
USEFUL FOR

Astronomers, physicists, and students of cosmology who are interested in the mathematical foundations of the Friedmann equations and their applications in understanding the universe's expansion.

Seetesh
Messages
1
Reaction score
0
I would like some help in calculating the basic Friedman equations starting from the flat FRW universe line element, Once I have calculated the Christoffel symbols for this metric how do i get to the Friedman equation, any link to a good book will be really helpful, thanks, seetesh.
 
Space news on Phys.org
Are you familiar with the Einstein Field Equations? The Friedmann equation comes from the 0-0 component.
 
Seetesh said:
I would like some help in calculating the basic Friedman equations starting from the flat FRW universe line element, Once I have calculated the Christoffel symbols for this metric how do i get to the Friedman equation, any link to a good book will be really helpful, thanks, seetesh.

Like Cristo said, it's the 00 component of Einstein equation so you will have to calculate

[tex]R_{00} - \frac{1}{2} g_{00} R[/tex]

and set this equal to the zeroth component of the stress energy momentum tensor times 8 pi G
 

Similar threads

  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 25 ·
Replies
25
Views
4K
  • · Replies 4 ·
Replies
4
Views
3K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 13 ·
Replies
13
Views
3K
Replies
22
Views
6K
  • · Replies 22 ·
Replies
22
Views
5K
  • · Replies 16 ·
Replies
16
Views
2K
  • · Replies 3 ·
Replies
3
Views
4K
Replies
14
Views
4K