- #1

Rick89

- 47

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Hi,

I am having some problems understanding this concept, I hope you can help.

I studied on Hobson, Efstathiou and Lasenby, in chapter 16 on Inflationary cosmology that in cosmological perturbation theory we need to express quantities in a gauge invariant way, very clear so far. The problem there is: we have a scalar field perturbation [itex] \phi (t) -> \phi_0 (t) +\delta\phi (t,x)[/itex] and we assume a perturbed metric from the flat background FRW which is [itex] ds^2=(1+2\Phi)dt^2 -(1-2\Phi) R(t)^2 (dx^2+dy^2+dz^2) [/itex] ,where [itex]\Phi [/itex] is the small perturbation.

They set about to derive a gauge invariant related to these quantities and derive what they call the curvature perturbation:

[itex]\Phi+ H\delta \phi / \phi_0 (t)' [/itex]

where [itex] \phi_0' [/itex] denotes the time derivative of [itex] \phi_0 [/itex] and H is the Hubble parameter. They then work in terms of this curvature perturbation saying that it does not depend on the coordinates used for the perturbation and so it can be done. I would like to understand how to obtain and how to understand that curvature perturb. That piece of the text is very unclear in my opinion, everything else in the book is very clear and well written, at least for undergrads... Thanx

I am having some problems understanding this concept, I hope you can help.

I studied on Hobson, Efstathiou and Lasenby, in chapter 16 on Inflationary cosmology that in cosmological perturbation theory we need to express quantities in a gauge invariant way, very clear so far. The problem there is: we have a scalar field perturbation [itex] \phi (t) -> \phi_0 (t) +\delta\phi (t,x)[/itex] and we assume a perturbed metric from the flat background FRW which is [itex] ds^2=(1+2\Phi)dt^2 -(1-2\Phi) R(t)^2 (dx^2+dy^2+dz^2) [/itex] ,where [itex]\Phi [/itex] is the small perturbation.

They set about to derive a gauge invariant related to these quantities and derive what they call the curvature perturbation:

[itex]\Phi+ H\delta \phi / \phi_0 (t)' [/itex]

where [itex] \phi_0' [/itex] denotes the time derivative of [itex] \phi_0 [/itex] and H is the Hubble parameter. They then work in terms of this curvature perturbation saying that it does not depend on the coordinates used for the perturbation and so it can be done. I would like to understand how to obtain and how to understand that curvature perturb. That piece of the text is very unclear in my opinion, everything else in the book is very clear and well written, at least for undergrads... Thanx

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