Axion Landscape and Natural Inflation

TL;DR

The paper proposes that a landscape of multiple axions with diverse shift-symmetry breaking terms can support eternal inflation, with bubble nucleation populating many vacua and a subsequent slow-roll phase along a flat direction generated by the KNP alignment. Vacuum analysis reveals numerous local minima whose energies tend toward a Gaussian distribution as the number of sources grows, and a very light inflaton direction emerges, yielding an enhanced decay constant; this sets the stage for large-field inflation after tunneling. Depending on the decay constant and modulations, the inflationary dynamics can resemble natural or multi-natural inflation, with the large-constant limit approaching quadratic chaotic inflation, though observational evidence for shorter inflation or deviations in n_s and r could reveal bubble-nucleation remnants and modulation-induced running of the spectral index. The work also discusses reheating, potential non-Gaussianity, and string-theory considerations, offering a unified picture of eternal and slow-roll inflation in the axion landscape and outlining observable signatures and model-building caveats.

Abstract

Multiple axions form a landscape in the presence of various shift symmetry breaking terms. Eternal inflation populates the axion landscape, continuously creating new universes by bubble nucleation. Slow-roll inflation takes place after the tunneling event, if a very flat direction with a super-Planckian decay constant arises due to the alignment mechanism. We study the vacuum structure as well as possible inflationary dynamics in the axion landscape scenario, and find that the inflaton dynamics is given by either natural or multi-natural inflation. In the limit of large decay constant, it is approximated by the quadratic chaotic inflation, which however is disfavored if there is a pressure toward shorter duration of inflation. Therefore, if the spectral index and the tensor-to-scalar ratio turn out to be different from the quadratic chaotic inflation, there might be observable traces of the bubble nucleation. Also, the existence of small modulations to the inflaton potential is a common feature in the axion landscape, which generates a sizable and almost constant running of the scalar spectral index over CMB scales. Non-Gaussianity of equilateral type can also be generated if some of the axions are coupled to massless gauge fields.

Figures (5)

• Figure 1: Distribution of axion potential $V(\phi_\alpha)$ at the found local minima in the units of $\Lambda^4$. We set $N_{\rm axion} = 8$, and we take $N_{\rm source} = 9, 11$ and $13$ from left to right. Each distribution is for one realization of the axion landscape satisfying $R < 10^{-2}$.
• Figure 2: Distribution of the difference of energy density ($\Delta V$) and the distance $D$ between each local minimum and its nearest adjacent one, in the units of $\Lambda^4$ and $f$, respectively. Here we used the axion landscape with $N_{\rm axion} = 8$ and $N_{\rm source} = 13$ in Fig. \ref{['energydistribution']}. The mean energy difference and distance are about $1.3 \Lambda^4$ and $1.4 f$, respectively.
• Figure 3: The three dimensional contour plot of the axion potential when the KNP mechanism is operative. The three axis $(\hat{\phi}_1, \hat{\phi}_2, \hat{\phi}_3)$ are chosen so that they coincide with the mass eigenstates at one of the local minima at the origin. Note that the scale of each axis is different, and the flat direction is approximately along the direction of $\hat{\phi}_1$.
• Figure 4: The schematic view of eternal inflation and subsequent slow-roll inflation in the axion landscape. The flat direction $\hat{\phi}_1$ arises due to the KNP mechanism and $\hat{\phi}_2$ collectively represents the other heavy modes. First, the Universe is stuck in one of the local minima, and eternal inflation takes place. After a certain point of time, (1) tunneling takes place, (2) heavy axions fast roll and oscillate, and (3) slow-roll inflation starts along the flat direction.
• Figure 5: The potential along the lightest axion direction in the axion landscape with (solid) or without (dashed) small modulations, which is due to an extra cosine function with a suppressed amplitude.