A question from a paper on perturbation theory

  • #1
Safinaz
259
8
TL;DR Summary
I try to read a paper on general relativity and perturbation theory:

https://arxiv.org/pdf/2109.01398.pdf#page16

My question is about equation (3.16) in section (3.2):

##
\delta \phi = -\sqrt{\frac{2}{\epsilon}} \left( \Phi+ \frac{\Phi’}{H} \right)
##
Where ##\delta \phi## is the first-order perturbation of a scalar field, ##\Phi## is the first-order perturbation of the space-time metric, and ##H## is the universe’s scale factor. It’s mentioned that this relation is given in reference:

https://arxiv.org/pdf/1002.0600.pdf

But I can't find such a relation in that reference. So I appreciate if someone had more experience in perturbation theory help me find out how this equation can be derived or proved from : https://arxiv.org/pdf/1002.0600.pdf
 
Last edited:
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  • #2
ok it may help to look at the equation in regards to the constraints to a single scalar field. Now while the second paper doesn't show that equation specifically it does provides the momentum constraints in section B see 33,34,35
further detail can be referenced by the second papers reference "Non-Gaussian features of primordial fluctuations in single field inflationary models" reference 3 of the second paper see section 2.4
https://arxiv.org/pdf/astro-ph/0210603.pdf

hope that helps
edit the H is likely the Hamilton in that equation as opposed to the Hubble parameter.
 

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