Exact Renormalisation Group Evolution of the Inflation Dynamics: Reconciling $α$-Attractors with ACT

TL;DR

This work tackles reconciling $\alpha$-attractor inflation, particularly E-models, with ACT data by incorporating quantum corrections through a non-perturbative functional renormalisation group (FRG) treatment of the inflaton. It develops a Wetterich-type flow on a time-dependent cutoff in a FLRW background, performing space coarse-graining to obtain a running potential $U_k(\phi)$ that couples to the Friedmann dynamics, and introduces $F=\partial_H U$ as a key variable. In the Local Potential Approximation with a Litim regulator, the analysis yields the Euclidean flow $\partial_\kappa U_\kappa(\phi)=\frac{aT^{-1}}{6\pi^2}{\cal D}_E^{-1}(a^{-1}\kappa^4)$ with ${\cal D}_E=-\frac{d^2}{dt^2}-3H\frac{d}{dt}+\kappa^2+\partial^2_\phi U_\kappa(\phi)$, and a real-time master equation $\ddot F+H\dot F+\left(\frac{\partial^2_\phi U}{H^2}-H^2-\dot H\right)F=\frac{H_0H^4}{6\pi^2}$ that couples to modified Friedmann equations. Numerically, they show that the RG flow destabilises the slow-roll trajectory, causing an earlier end to inflation and placing horizon exit at larger $\phi$, thereby shifting the predicted spectral index $n_s$ toward the ACT-preferred region. Consequently, the $\alpha$-attractor E-models can be brought into agreement with ACT data without introducing new physics beyond a consistent quantum-corrected inflaton dynamics.

Abstract

We present a non-perturbative framework for the dynamics of slow-roll inflation that consistently incorporates quantum corrections, based on an alternative functional renormalisation group (RG) approach. We derive the coupled Friedmann-RG flow equations governing the joint evolution of spacetime, the inflaton field, and its effective potential. Applying this formalism to $α$-attractor E-models, we find that the RG flow induces a dynamical destabilisation of the inflationary trajectory, leading to a premature termination of slow roll. Remarkably, the resulting predictions bring $α$-attractors into full agreement with the latest ACT data without introducing new physics beyond a consistent quantum-corrected treatment of the inflaton dynamics.

Figures (2)

• Figure 1: Full ERG evolution of the potential $U(\phi,H(N))$ (coloured lines), for $\alpha=0.1$, $\phi_0=2.3M_p$, and for various values of the number of $e$-folds since horizon crossing (assumed to be at $\phi(0)=\phi_0$). Coloured dots depict the corresponding values of the solution $\phi(N)$ when these potentials are evaluated.
• Figure 2: Tensor-to-scalar ratio $r$ as a function of the spectral index $n_s$ calculated with (right panel) or without (left panel) including the ERG flow of the potential.