A review of Axion Inflation in the era of Planck

TL;DR

The review surveys axion-based inflation models that leverage a shift symmetry to stabilize slow-roll against Planck-scale corrections, covering natural inflation, monodromy, multi-axion alignments, and gauge-field–driven dynamics. It connects these constructions to Planck-era constraints and highlights distinctive predictions, including potentially chiral gravitational waves, oscillatory signatures in the power spectrum and higher-point functions, non-Gaussianities, and primordial black holes. A key theme is how non-perturbative effects and gauge-field couplings imprint observable signals, while backreaction and theoretical bounds on the axion decay constant constrain the viable parameter space. The work emphasizes future tests from CMB polarization, gravitational-wave detectors, and large-scale structure as critical for distinguishing among axion inflation scenarios and for assessing the role of shift symmetry in early-universe dynamics.

Abstract

Because the inflationary mechanism is extremely sensitive to UV-physics, the construction of theoretically robust models of inflation provides a unique window on Planck-scale physics. We review efforts to use an axion with a shift symmetry to ensure a prolonged slow-roll background evolution. The symmetry dictates which operators are allowed, and these in turn determine the observational predictions of this class of models, which include observable gravitational waves (potentially chiral), oscillations in all primordial correlators, specific deviations from scale invariance and Gaussianity and primordial black holes. We discuss the constraints on this class of models in light of the recent Planck results and comment on future perspectives. The shift symmetry is very useful in models of large-field inflation, which typically have monomial potentials, but it cannot explain why two or more terms in the potential are fine-tuned against each other, as needed for typical models of small-field inflation. Therefore some additional symmetries or fine-tuning will be needed if forthcoming experiments will constrain the tensor-to-scalar ratio to be r < 0.01.

Figures (2)

• Figure 1: The figure, taken from PlanckInfl shows the $68\%$ and $95\%$ CL contours form Planck plus various ancillary sets of data (indicated in the right panel) in the tensor-to-scalar ratio $r$ vs scalar spectral tilt $n_{s}$. Shown are also several inflationary models. In the main text we discuss those potential that arise for axions, i.e. $\phi^{2/3}, \phi,\phi^{2}$ and natural inflation.
• Figure 2: The left plot, taken from Linde:2012bt, shows the primordial scalar power spectrum as function of efoldings before the end of inflation including the corrections coming from the inverse decay of gauge fields together with the upper bound coming from the constraints on primordial black holes. We note a growth of the power spectrum with decreasing scales (corresponding to decreasing $N$) from the COBE normalized value to the saturation value (\ref{['zeta-strong']}) in the strong backreaction regime. The right plot, taken from BPP, shows the fraction of the total energy density in terms of primordial gravitational waves as function of frequency produced by the inverse decay of gauge fields for the three indicated values of $\xi$ and a linear potential. Also in this case we signal grows at decreasing scales (corresponding to higher frequencies. For comparison we also show the expected sensitivity of three gravitational wave experiments (see BPP for details).