Back Reaction Of Perturbations In Two Scalar Field Inflationary Models

TL;DR

This work studies the back-reaction of long-wavelength cosmological perturbations on the local expansion rate Θ in a two-field inflationary setup with an inflaton φ and a clock field χ. By deriving Θ to second order and evaluating on χ-constant surfaces, the authors show that the leading infrared back-reaction terms generally do not vanish, and can be enhanced when entropy modes are active. Using adiabatic and entropy-mode scenarios, they demonstrate clock-dependent behavior: choosing χ as a clock can yield observable back-reaction with potential sign changes depending on the clock choice, and entropy modes in hybrid-like models can even dominate the evolution of Θ. These findings provide evidence that infrared fluctuations can have locally observable effects and motivate further quantitative assessment of their impact on inflationary predictions and late-time cosmology.

Abstract

We calculate the back-reaction of long wavelength cosmological perturbations on a general relativistic measure of the local expansion rate of the Universe. Specifically, we consider a cosmological model in which matter is described by two scalar matter fields, one being the inflaton and the other one representing a matter field which is used as a clock. We analyze back-reaction in a phase of inflaton-driven slow-roll inflation, and find that the leading infrared back-reaction terms contributing to the evolution of the expansion rate do not vanish when measured at a fixed value of the clock field. We also analyze the back-reaction of entropy modes in a specific cosmological model with negative square mass for the entropy field and find that back-reaction can become significant. Our work provides evidence that, in general, the back-reaction of infrared fluctuations could be locally observable.