- #1

Zag

- 49

- 9

I have been studying perturbation theory in the context of FRW cosmologies, and so far have had a really hard time understanding why the SVT (Scalar, Vector, and Tensor) perturbations associated with the metric tensor "decouple" at first order in perturbation theory.

All references avoid explaining this crucial step and simply jump to the final results by mentioning something along the lines: "Because the perturbations decouple, we can write these equations of motion for the scalars, and these equations over here for the vectors, etc."

However, it is not clear to me at all why these 3-scalars, 3-vectors, and 3-tensors which encapsulate the perturbations should evolve independently. In fact, Einstein equations mix them all into the same equation of motion, namely the field equations of general relativity. What is the argument to separate these perturbations into different equations? Where can I find a rigorous mathematical treatment which is not outdated?

Thanks a lot! Any reference and/or comment is appreciated.Zag