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Tensor to scalar ratio of perturbation amplitudes and inflaton dynamics
For the inflaton perturbations it is shown that the evolution of the
difference between the spectral indices can be translated into information on
the scale dependence of the tensor to scalar amplitudes ratio, , and how the
scalar field potential can be derived from that information. Examples are given
where converges to a constant value during inflation but dynamics are
rather different from the power--law model. Cases are presented where a
constant is not characteristic of the inflationary dynamics though the
resulting perturbation spectra are consistent with the CMB and LSS data.
The inflaton potential corresponding to given by a n--th order polynomial
of the e--folds number is derived in quadratures expressions. Since the
observable difference between the spectral indices evaluated at a pivot scale
yields information about the linear term of that polynomial, the first order
case is explicitly written down. The solutions show features beyond the
exponential form corresponding to power--law inflation and can be matched with
current observational data.Comment: 5 two-columns pages, two figures, RevTex4. Minor modifications. Two
references adde
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