- #1
thecommexokid
- 70
- 2
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:
[tex]P_{\mathcal{R}}(k)=\frac{4\pi}{\epsilon(\eta_k)}\bigg( \frac{H(\eta_k)}{2\pi} \bigg)^2,[/tex]
where:
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.
[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,
- k is the comoving wavenumber of the mode,
- ε is the slow-roll parameter,
- H is the Hubble parameter, and
- ηk is the (conformal) time when the mode [itex]\mathcal{R}_k[/itex] exited the horizon.
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.