Clarify the name of coherent enhancement mechanism

[maxitg]

Clarify the name of Coherent Enhancement Mechanism

Referee 1:
Superficially, this paper appears to claim to have a way to evade this
bound--to produce a model with a large effective axion decay constant
that nonetheless is consistent with the fundamental bound on axion
field ranges arising from the Weak Gravity Conjecture. The authors
refer to this as a "Coherent Enhancement Mechanism," which suggests a
way to obtain a large field range similar to past models like
N-flation or KNP alignment. On closer inspection, however, the models
in this paper do nothing of the sort. Rather, they produce inflation
over a small field range, f < M_planck, by forming a potential by a
sum of cosine terms which are comparably large and so can
approximately cancel in some regions to produce models that are
effectively of inflection-point or plateau type.

Perhaps I should return briefly to the authors' phrase "Coherent
Enhancement Mechanism," which is highly misleading. What they claim to
enhance is an "effective decay constant" which is just a ratio of the
Planck scale to the square root of a linear combination of slow roll
parameters. This is not an effective decay constant in any standard
sense; for instance, it has nothing to do with periods of cosine terms
or of how far the inflaton evolves during inflation. When they claim
to achieve a super-Planckian effective decay constant, they only mean
that they have a model of slow-roll inflation. But there are many such
models, and the models of this paper do not improve in any interesting
conceptual way on them.

Referee 2:
The authors emphasize multiple times that they provide a mechanism to enhance the de- cay constant to transplanckian values even if the fundamental axionic periodicity f is sub- planckian, therefore providing an axion inflationary model with cosine terms that is com- patible with the WGC. This makes the reader think that they have managed to construct an effective model of natural inflation in which the axionic field range is transplanckian but still consistent with the Weak Gravity Conjecture. However, in the caption of Figure 1, they explain that the field range is in fact smaller than the fundamental periodicity f and, therefore, subplanckian (which explains why r is so small in the plots). This means that they have constructed instead a small field inflationary model from a superposition of many cosine terms. But then, it does not look so impressive that they evade the WGC (of course, the WGC is compatible with ∆φ < f < Mp!) and I find very misleading the presentation of the paper. My first question to the authors is whether my above interpre- tation of their results is correct and whether the field range is also subplanckian in the supergravity model. If so, I think they should modify the whole phrasing of the paper to clarify that the field range is always subplanckian and therefore, trivially compatible with the WGC, as the ’enhancement of the effective decay constant’ is not correlated to the field range.