content_image/349726.jpg content_image/349727.jpg content_image/349728.jpg content_image/349733.jpg content_image/349734.jpg
in [203, 204] $^{9}$: 

<img src='content_image/349726.jpg'>

It gives for the slow-roll parameter ϵ$_{1}$ = − ˙ H/H $^{2}$, and inflation takes place only when ¨ a > 0 which is equivalent to ϵ$_{1}$ < 1. Slow-roll inflation takes place when ∀ n, ϵ$_{n}$ ≪ 1. In the slow-roll limit, these parameters can be related to the slow-roll parameters, 

<img src='content_image/349727.jpg'>

Transient violation of slow-roll conditions were studied in hybrid inflation [206], for com- putation of the power spectrum, see [207, 208]. Models of inflation with large η were also considered in [151]. 

## 4. Gravitational waves 

Gravitational waves are linearized tensor perturbations of the metric and do not couple to the energy momentum tensor. Therefore, they do not give rise a gravitational instability, but carry the underlying geometric structure of the space-time. The first calculation of the gravitational wave production was made in [14], and the topic has been considered by many authors [15–17]. For reviews on gravitational waves, see [12, 209]. 

The gravitational wave perturbations are described by a line element ds 2 + δds $^{2}$, where 

<img src='content_image/349728.jpg'>

The gauge invariant and conformally invariant 3-tensor h$_{ij}$ is symmetric, traceless δ $^{ij}$h$_{ij}$ = 0, and divergenceless ∇ $_{i}$h$_{ij}$ = 0 ( ∇ i is a covariant derivative). Massless spin 2 gravitons have two degrees of freedom and as a result are also transverse. This means that in a Fourier domain the gravitational wave has a form 

<img src='content_image/349733.jpg'>

For the Einstein gravity, the gravitational wave equation of motion follows that of a massless Klein Gordon equation [12]. Especially, for a flat universe 

<img src='content_image/349734.jpg'>

