Simple exercises to flatten your potential

TL;DR

The paper analyzes how backreaction from heavy fields on the inflationary sector can systematically flatten an otherwise quadratic inflaton potential, with the heavy modes adjusting to minimize energy. Using a simple two-field toy model and several string-theoretic axion monodromy scenarios, it shows that the effective potential can transition toward linear or sub-quadratic forms (V(φ) ∝ φ^p with p<2) at large φ, while maintaining moduli stabilization. It outlines multiple backreaction channels—flux rearrangements (Bowflux), running kinetic terms, and moduli backreaction (Weight lifting)—and even speculative multi-throat setups (Circuit training) that yield various flattened power laws (e.g., V ∝ φ^{6/5} or φ^{4/5}). The results provide a framework for embedding large-field inflation in UV-complete string compactifications and offer testable links to CMB observables, where future data could tighten constraints on the inflaton's couplings to heavy fields.

Abstract

We show how backreaction of the inflaton potential energy on heavy scalar fields can flatten the inflationary potential, as the heavy fields adjust to their most energetically favorable configuration. This mechanism operates in previous UV-complete examples of axion monodromy inflation - flattening a would-be quadratic potential to one linear in the inflaton field - but occurs more generally, and we illustrate the effect with several examples. Special choices of compactification minimizing backreaction may realize chaotic inflation with a quadratic potential, but we argue that a flatter potential such as power-law inflation $V(φ) \propto φ^p$ with $p<2$ is a more generic option at sufficiently large values of $φ$.

Figures (2)

• Figure 1: Combined data constraints on the tensor to scalar ratio $r$ and the tilt $n_s$Observations together with the predictions for power-law potentials $\propto \phi^p\;,\;p>0$ for 50 e-foldings (green line) and 60 e-foldings (blue line) of inflation. Flattening the potential corresponds to moving down and to the right along these lines. The colored points denote powers that have arisen in various large-field monodromy inflation models in string theory: IIB linear axion monodromy from 5-branes (squares; $\phi$), IIA moving 4-brane monodromy (diamonds; $\phi^{2/3}$), and a candidate example of IIB flux axion monodromy (this work; triangles; $\phi^{4/5}$).
• Figure 2: Effects of an inflationary flux on the three-term structure stabilized in a Minkowski minimum for $x = 0$.