A New Angle on Chaotic Inflation

TL;DR

The paper addresses realizing large-field inflation in theories with many axions (N-flation) when individual decay constants are sub-Planckian. It introduces kinetic alignment, showing that a randomly mixed kinetic term (e.g., Wishart-like $K_{ij}$) generically aligns the maximal eigenvector with a long diagonal, yielding an effective field range $\Delta\Phi\approx\sqrt{N}\,f_N$ (or $\sqrt{P}\,f_N$ when $P$ mass terms participate). Under plausible mass-term hierarchies, this alignment persists, allowing inflation to proceed along aligned directions and often reducing to single-field chaotic inflation with $V\sim m^2\Phi^2$, predicting $n_s\approx0.967$ and $r\approx0.13$ for $N_e=60$. This mechanism significantly eases embedding N-flation in string theory by decoupling the need for many large decay constants and providing robust observational signatures similar to simple chaotic inflation.

Abstract

N-flation is a radiatively stable scenario for chaotic inflation in which the displacements of $N \gg 1$ axions with decay constants $f_1 \le \ldots \le f_N < M_P$ lead to a super-Planckian effective displacement equal to the Pythagorean sum $f_{Py}$ of the $f_i$. We show that mixing in the axion kinetic term generically leads to the phenomenon of kinetic alignment, allowing for effective displacements as large as $\sqrt{N} f_{N} \ge f_{Py}$, even if $f_1, \ldots, f_{N-1}$ are arbitrarily small. At the level of kinematics, the necessary alignment occurs with very high probability, because of eigenvector delocalization. We present conditions under which inflation can take place along an aligned direction. Our construction sharply reduces the challenge of realizing N-flation in string theory.

Figures (2)

• Figure 1: N-flation with and without alignment, for $N=2$. The outer box shows a fundamental domain in the dimensionless $\theta$ coordinates with period $2\pi$. The shaded rhombus and rectangle depict the physical size of the fundamental domain with and without alignment, respectively. The green and red vectors show the semidiameters in the aligned and unaligned cases. The inset is not to scale.
• Figure 2: Attractor behavior for $N=2$, with axes as in fig. 1. The red (green) curves are inflating (non-inflating) trajectories. Curves beginning outside the circle yield $N_{e} \ge 55$.