content_image/361615.jpg content_image/361616.jpg content_image/361617.jpg content_image/361618.jpg content_image/361619.jpg content_image/361620.jpg content_image/361622.jpg
a critical density universe, if we assume that the primordial spectrum can be approximated by a power law (ignoring the gravitational waves and the k − dependence of the power n$_{s}$ ) [13] 

<img src='content_image/361615.jpg'>

where n$_{s}$ is called the spectral index (or spectral tilt), the reference scale is: k$_{0}$ = 7 . 5 a$_{0}$H$_{0}$ ∼ 0 . $_{002 Mpc}$− $^{1}$, and the error bar on the normalization is given at 1 σ . The spectral index n ( k ) is defined as 

<img src='content_image/361616.jpg'>

This definition is equivalent to the power law behavior if n ( k ) is close to a constant quantity over a range of k of interest. One particular value of interest is n$_{s}$ ≡ n ( k$_{0}$ ). If n$_{s}$ = 1, the spectrum is flat and known as Harrison-Zeldovich spectrum [200, 201]. For n$_{s}$ ̸ = 1, the spectrum is tilted, and n$_{s}$ > 1 ( n$_{s}$ < 1) is known as a blue (red) spectrum. In the slow-roll approximation, this tilt can be expressed in terms of the slow-roll parameters and at first order 8 

The running of these parameters are given by [156] 

<img src='content_image/361617.jpg'>

<img src='content_image/361618.jpg'>

where 

<img src='content_image/361619.jpg'>

Slow-roll inflation requires that ϵ ≪ 1 , | η | ≪ 1, and therefore naturally predicts small variation in the spectral index within Δ ln k ≈ 1 [202] 

<img src='content_image/361620.jpg'>

Independently of slow-roll considerations or of the number of fields involved in the dynamics of inflation, a new set of parameters, known as the Hubble-flow parameters, were discussed 

<img src='content_image/361622.jpg'>

