The single scalar field inflationary models that lead to scalar and tensor
perturbation spectra with amplitudes varying in direct proportion to one
another are reconstructed by solving the Stewart-Lyth inverse problem to
next-to-leading order in the slow-roll approximation.
The potentials asymptote at high energies to an exponential form,
corresponding to power law inflation, but diverge from this model at low
energies, indicating that power law inflation is a repellor in this case. This
feature implies that a fine-tuning of initial conditions is required if such
models are to reproduce the observations. The required initial conditions might
be set through the eternal inflation mechanism.
If this is the case, it will imply that the spectral indices must be nearly
constant, making the underlying model observationally indistinguishable from
power law inflation.Comment: 20 pages, 7 figures. Major changes to the Introduction following
referee's comments. One figure added. Some other minor changes. No conclusion
was modifie