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246 EXACT SOLUTIONS AND SCALAR FIELDS IN GRAVITY
is based on the ratio between the slow-roll parameters and their respective
differences. When the value of the parameters is much greater
than the difference between any pair of parameters, a generalization of
the standard Bessel approximation takes place. We called this approach
generalized power-law approximation. In the opposite case, when the
value of the parameters is much less than their difference, a similar
approach (generalized slow-roll approximation) can be used. These approximations
plus the standard approximation cover a large space of
inflationary models.
The obtained expressions were tested against the known exact results
for power-law and natural inflation. A more rigorous test allowing to
determine the contribution of higher corrections will be carried out in a
forthcoming paper.
Acknowledgments
This research was supported by CONACyT Grant: 32138E.
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