For scalar modes [itex]\mathcal{R}_k[/itex] originating in the Bunch-Davies vacuum at the onset of inflation, I have the following equation for their primordial power spectrum:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]P_{\mathcal{R}}(k)=\frac{4\pi}{\epsilon(\eta_k)}\bigg( \frac{H(\eta_k)}{2\pi} \bigg)^2,[/tex]

where:

c=G=ħ= 1,kis the comoving wavenumber of the mode,εis the slow-roll parameter,His the Hubble parameter, andηis the (conformal) time when the mode [itex]\mathcal{R}_k[/itex] exited the horizon._{k}

In my notes, I have this equation labeled as "Well-known result:", but now I am struggling to even find a source for it. Can anyone offer any assistance in finding a reference for this? My goal is to have some understanding of its derivation.

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# Primodial power spectrum of scalar perturbations

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