Trajectories with suppressed tensor-to-scalar ratio in Aligned Natural Inflation

TL;DR

This paper explores how aligned natural inflation models can produce suppressed tensor-to-scalar ratios by utilizing saddle point inflation trajectories, aligning with current CMB observations.

Contribution

It introduces a general two-axion potential framework with four parameters, demonstrating the possibility of saddle point inflation with low tensor-to-scalar ratios.

Findings

Inflation can occur along valleys ending in minima, similar to single-field models.

Higher altitude saddle point trajectories can produce low tensor-to-scalar ratios.

The model's predictions align with current CMB constraints on $n_s$ and $r$.

Abstract

In Aligned Natural Inflation, an alignment between different potential terms produces an inflaton excursion greater than the axion scales in the potential. We show that, starting from a general potential of two axions with two aligned potential terms, the effective theory for the resulting light direction is characterized by four parameters: an effective potential scale, an effective axion constant, and two extra parameters (related to ratios of the axion scales and the potential scales in the $2-$field theory). For all choices of these extra parameters, the model can support inflation along valleys (in the $2-$field space) that end in minima of the potential. This leads to a phenomenology similar to that of single field Natural Inflation. For a significant range of the extra two parameters, the model possesses also higher altitude inflationary trajectories passing through saddle points of the $2-$field potential, and disconnected from any minimum. These plateaus end when the heavier direction becomes unstable, and therefore all of inflation takes place close to the saddle point, where - due to the higher altitude - the potential is flatter (smaller $\epsilon$ parameter). As a consequence, a tensor-to-scalar ratio $r = {\rm O } \left( 10^{-4} - 10^{-2} \right)$ can be easily achieved in the allowed $n_s$ region, well within the latest $1 \sigma$ CMB contours.