The UV Sensitivity of Axion Monodromy Inflation

1. Clear physical point: periodic modulations introduce a high-frequency scale that can invalidate the usual “integrate out heavy moduli” logic when the modulation frequency competes with the modulus mass.
2. Concrete, string-motivated two-field setup (modulus-dependent kinetic term + modulated axion potential) that makes the UV-sensitivity mechanism explicit. 3.Provides analytic control of the “wiggly” background (oscillatory corrections to the inflaton/modulus evolution). 4.Phenomenology payoff: predicts an oscillatory squeezed-limit bispectrum (resonant-collider type) that could motivate targeted searches

1. Validity and backreaction: when ω ≳ m the heavy modulus is continuously excited; please clarify the energy budget, whether slow roll is maintained, and the conditions preventing modulus destabilization.
2. Model assumptions: the text notes other neglected couplings that could induce oscillatory corrections to the modulus mass; please justify why omitting them does not qualitatively change the resonance/conclusions, or delineate the affected parameter range. 3.Self-contained perturbation/bispectrum evidence: since key steps are deferred to a companion paper, add at least one limiting-case cross-check (e.g., b*→0 / decoupling) or a brief roadmap of the derivation to strengthen confidence in the main bispectrum claim 4.Observational template and distinguishability: the bispectrum shows multiple oscillatory dependences; please comment on distinguishability from standard feature/resonant/collider templates and on viable parameter space once current constraints are imposed.

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1- Above equation (9), it is claimed that the dominant oscillatory cubic interaction comes from the $\dot{\lambda}\pi \dot{\pi}\sigma$ term, using $\dot{\lambda} = \omega \lambda$. However, $\lambda(t)$, being the total field velocity $\dot{\Phi}_t$ (multiplied by the turning rate $\Omega$), is dominated by $\dot{\phi}_0$ and does not satisfy $\dot{\lambda} = \omega \lambda$; I would think that it should be suppressed by the ratio $\dot{\phi}_1/\dot{\phi}_0$.

2- Regardless of whether the $\dot{\lambda}\pi \dot{\pi}\sigma$ is enhanced with respect to $\lambda (\partial_{\mu}\pi)^2\sigma$ term, $\lambda$ consists of a leading, non-oscillatory $\dot{\phi}_0$ piece and subleading, oscillatory $\dot{\phi}_1$ and $\dot{\rho}_1$ pieces, so I think the cubic vertex in (9) should have similar $\bar{g}+g_3$ structure as the linear mixing $\bar{g}+g_2$. In [19] it is shown that an oscillatory linear mixing is essential to an enhanced bispectrum, hence it is important to include the oscillatory $g_2$ coupling even though it is subleading. It should be clarified whether it is the same case for $g_3$, where the subleading oscillatory piece is important compared to the leading, non-oscillatory piece for the cosmological collider signal.

3- Moreover, given that the authors have emphasized the presence of this oscillatory cubic interaction throughout the paper as an important distinction from the results in [19], I think the effect of the oscillatory cubic vertex $g_3$ in the cosmological collider signal should be discussed more explicitly, instead of being lumped together with $g_2$.

4- In the calculation of the background field trajectory around equation (6), the estimate of the size of $\rho$ oscillation $B\simeq b_* f^2/\Lambda$ relies on $\omega$ to be greater than but close to $m$, such that $\Xi^4 = 9\omega^2 H^2 + (\omega^2-m^2)^2 \approx 9 \omega^2 H^2$ instead of $\Xi^4 \approx \omega^4$. If $\omega \gg m$, $B$ would be further suppressed by a factor of $H/\omega$. Is the need for $\omega$ to be close to $m$ important for any of the subsequent analysis and cosmological collider signal?

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