Dilaton-Flattened Axion Inflation

Abstract

We present a solvable same-sector effective theory for anomaly-inspired axion inflation, in which a heavy trace-anomaly mode dynamically backreacts on the axion potential. The tree-level elimination of the radial field resums the backreaction into a closed-form Lambert-$W$ potential, naturally flattening the hilltop potential without external plateau operators. By deriving the exact trough metric, we evaluate all the observables on the fully reduced one-field action, bypassing uncontrolled kinetic approximations. Calibrated at $N_{\star }=56$, reheating-compatible branches yield $r\simeq 0.033$--$0.036$ and $\hat{I}{\pm }_s\simeq -(4.6$--$4.7)\times 10^{-4}$, comfortably satisfying the current ACT/SPT/BICEP constraints. The evolution remains strictly adiabatic ($m_{\perp }^2/H^2\gtrsim 6.1$, $\hat{I}\text{c◯}/H\lesssim 7.6\times 10^{-4}$) with negligible sound-speed and metric corrections. We provide analytic control over the constant-$w_{\mathrm{eff}}$ reheating map, the $N_{\mathrm{re}}=0$ boundary, and robustness against vacuum-offset deformations. This Lambert-$W$ backbone establishes a precise, deformable benchmark for confining axion inflation, with microscopic matching and reheating microphysics accessible as systematic EFT refinements.

13,13 any comments are welcome