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The spectrum of cosmological perturbations produced by a multi-component inflaton to second order in the slow-roll approximation
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We derive general analytic formulae for the power spectrum and spectral index of the curvature perturbation produced during inflation driven by a multi-component inflaton field, up to the second order in the slow-roll approximation. We do not assume any specific properties of the potential or the metric on the scalar field space, except for the slow-roll condition, Einstein gravity, and the absence of any permanent isocurvature modes.
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Cited by 3 Pith papers
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The Dual Primordial Black Hole Formation Scenario
A single small-scale perturbation can form ultralight black holes during a break in inflation and heavier black holes after inflation, linking reheating to dark matter.
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On the Validity of the Effective Theory of (Multi-)Field Inflation
Computes perturbation amplitudes in general effective multi-field inflation without sub-horizon limit and bounds higher-derivative corrections via ε for finite-cutoff models.
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Comment on: "Third-order corrections to the slow-roll expansion: Calculation and constraints with Planck, ACT, SPT, and BICEP/Keck [2025 PDU 47 101813]"
Several terms in the third-order slow-roll power spectra are incorrect because three-dimensional integrals were evaluated by integrating a truncated Taylor expansion instead of Taylor-expanding the integral.
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