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Constraints on the Sharpness of the Curvature Power Spectrum
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Motivated by the fact that a sharply peaked curvature spectrum is often considered in the literature, we examine theoretical constraints on the sharpness of such a spectrum. In particular, we show that the sharply peaked curvature power spectrum, originating from the enhancement of subhorizon perturbations during inflation, is significantly constrained by energy conservation. While the constraints do not depend on the exact form of inflaton potential, we also study concrete inflaton potentials that realize a sharply peaked curvature spectrum and how theoretical limits are saturated in these cases.
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Cited by 2 Pith papers
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How deep is the dip and how tall are the wiggles in inflationary power spectra?
In single-field PBH inflation models, a power-spectrum dip appears precisely when the inflaton velocity does not flip sign, and the peak amplitude scales as the inverse square of the dip amplitude.
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RG-Flow Renormalized One-Loop Corrections to the Power Spectrum in USR Inflation
A cutoff-regularized, in-in calculation of cubic, quartic, and tadpole one-loop corrections finds the USR fractional correction scales as P_CMB e^{6ΔN}, confirming the sharp-transition loop-enhancement debate's original side.
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