Inflation by Alignment

TL;DR

The paper addresses how large-field inflation can be achieved with pseudo-Goldstone inflatons by exploiting alignment between kinetic and potential directions. It develops a unified treatment of two main mechanisms—kinetic alignment and lattice alignment—first in compact two-axion natural inflation and then extended to noncompact pGBs with exponential potentials, including moduli-like scenarios. In the compact case, perfect kinetic alignment yields an effective decay constant $1/f_{\rm eff} = \lambda \sin(\omega/2)$, enabling super-Planckian field ranges and a spectrum of predictions that interpolate with $f_{\rm eff}$; in noncompact models, alignment can produce either large tensor modes or slow-roll along flat directions, depending on the alignment angle $\omega$ and the functional form of $U(\theta)$. Overall, the work shows alignment as a versatile, UV-embeddable mechanism to realize large-$f$ inflation across a broader class of models, including extra-dimensional moduli, with tangible implications for the tensor-to-scalar ratio $r$.

Abstract

Pseudo-Goldstone bosons (pGBs) can provide technically natural inflatons, as has been comparatively well-explored in the simplest axion examples. Although inflationary success requires trans-Planckian decay constants, f > Mp, several mechanisms have been proposed to obtain this, relying on (mis-)alignments between potential and kinetic energies in multiple-field models. We extend these mechanisms to a broader class of inflationary models, including in particular the exponential potentials that arise for pGB potentials based on noncompact groups (and so which might apply to moduli in an extra-dimensional setting). The resulting potentials provide natural large-field inflationary models and can predict a larger primordial tensor signal than is true for simpler single-field versions of these models. In so doing we provide a unified treatment of several alignment mechanisms, showing how each emerges as a limit of the more general setup.

Figures (4)

• Figure 1: The potential landscape \ref{['compact-potential']} for $\omega = \pi/4$ and $\lambda_1 = \lambda_2$ (left panel) and $\lambda_1 = \lambda_2 /2 = 1$ (right panel). Darker colours indicate lower values of $V$.
• Figure 2: The spectral index $n_s$ and tensor-to-scalar ratio $r$ (evaluated at 60 e-folds) for the effectively single-field models \ref{['eff-sin']} (dashed line) and \ref{['eff-tanh']} (dotted line) as a function of the effective decay constant.
• Figure 3: The potential landscape for \ref{['potential-tanh']} with $U(\theta) \propto \tanh \theta$ and for $\omega = \pi/4$ and $\lambda_1 = \lambda_2$ (left panel) and $\lambda_1 = \lambda_2 /2 = 1$ (right panel). Darker colours indicate lower values for the potential.
• Figure 4: The potential landscape for the choice (\ref{['expU']}) with $\omega = \pi/100$ and $A=\lambda_1 = \lambda_2=1$ (left panel) and $A=\lambda_1 = \lambda_2 /2 = 1$ (right panel). Darker colours indicate lower values of $V$.