Here, we give the state of the cosmological perturbations after the inflationary phase (that is, what is used as initial conditions in a CMB code such as CMBFAST and CAMB).

When the universe is matter- or radiation-dominated, the expansion is decelerating. This means that physical length, which grow as the scale factor, grow more slowly than the Hubble radius, so that a given mode "enters" into the Hubble radius at some time (i.e., it becomes smaller than the size of the observable universe and hence becomes observable). During inflation, the situation is opposite: expansion is accelerating and mode exit the Hubble radius at some time. Cosmological perturbations are generated precisely at the epoch where they exit the Hubble radius. When inflation ends, modes begin to reenter into the Hubble radius, and have the following properties:

 After their generation during the inflationary phase, the perturbation remain "frozen", they begin to evolve only long after inflation, when they reenter into the Hubble radius.

 They are Gaussian or almost Gaussian. Although this property is not necessary for inflation, it is the consequence of the simplest models.

 The fluctuations are seen as random variables, our universe density field being an example of a realization of these random variables. In the hypothesis where the fluctuations are Gaussian, the only relevant statistical quantity is the variance of the fluctuations. This variance is usually quoted in Fourier space, as modes with different wavevectors evolve independently from each other (at least in the linear regime) and is called the power spectrum. For the gravitational potential, the power spectra are likely to be close to power laws and therefore described by an amplitude A_S and A_T and a spectral index, n_S and n_T.

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