Inflationary Infrared Divergences: Geometry of the Reheating Surface vs. delta N Formalism

Abstract

We describe a simple way of incorporating fluctuations of the Hubble scale during the horizon exit of scalar perturbations into the delta N formalism. The dominant effect comes from the dependence of the Hubble scale on low-frequency modes of the inflaton. This modifies the coefficient of the log-enhanced term appearing in the curvature spectrum at second order in field fluctuations. With this modification, the relevant coefficient turns out to be proportional to the second derivative of the tree-level spectrum with respect to the inflaton phi at horizon exit. A logarithm with precisely the same coefficient appears in a calculation of the log-enhancement of the curvature spectrum based purely on the geometry of the reheating surface. We take this agreement as strong support for the proposed implementation of the delta N formalism. Moreover, our analysis makes it apparent that the log-enhancement of the inflationary power-spectrum is indeed physical if this quantity is defined using a global coordinate system on the reheating surface (or any other post-inflationary surface of constant energy density). However, it can be avoided by defining the spectrum using invariant distances on this surface.

13 pages, LaTeX. v3: Referencing improved

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Cited by in corpus (16)

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• Perturbative Quantum Gravity Comes of Age
• Cosmological UV/IR Divergences and de-Sitter Spacetime
• Issues Concerning Loop Corrections to the Primordial Power Spectra
• Quantum corrections to the primordial tensor spectrum: Open EFTs & Markovian decoupling of UV modes
• Hot Cosmic Qubits: Late-Time de Sitter Evolution and Critical Slowing Down
• Quantum backreaction in evolving FLRW spacetimes
• Infrared-finite graviton two-point function in static de Sitter space
• Large gauge transformation, Soft theorem, and Infrared divergence in inflationary spacetime
• IR Divergence in Inflationary Tensor Perturbations from Fermion Loops
• Conservation of superhorizon curvature perturbations at one loop: Backreaction in the in-in formalism and Renormalization
• Anisotropic separate universe and Weinberg's adiabatic mode
• Role of the counterterms in the conservation of superhorizon curvature perturbations at one loop
• Radiative Corrections from Heavy Fast-Roll Fields during Inflation
• Stochastic approach to gravitational waves from inflation