content_image/317710.jpg content_image/317711.jpg content_image/317714.jpg content_image/317715.jpg content_image/317712.jpg content_image/317713.jpg
in quasi-de Sitter inflation we have H ≈ constant , i.e. H varies extremely slowly with scale. We now transform from cosmic time t to conformal time 

and also consider instead the comoving field perturbation 

Eq. (3.40) now becomes 

where 

<img src='content_image/317710.jpg'>

<img src='content_image/317711.jpg'>

<img src='content_image/317714.jpg'>

<img src='content_image/317715.jpg'>

where we have assumed a ( t ) ∝ e $^{Ht}$. We have thus obtained a harmonic oscil- lator scenario. Following the usual procedure of QFT, we will now promote variables to operators and quantize this harmonic oscillator. We express the comoving perturbation in terms of Fourier components as 

<img src='content_image/317712.jpg'>

where ˆ a † and ˆ a are creation and annihilation operators respectively, that satisfy 

<img src='content_image/317713.jpg'>

