Natural and Multi-Natural Inflation in Axion Landscape

TL;DR

The paper addresses how a landscape of axions with multiple shift-symmetry breaking terms can yield slow-roll inflation after false-vacuum decay, potentially reconciling a large tensor-to-scalar ratio with Planck constraints. It shows that a super-Planckian effective decay constant $f_{ m eff}$ can arise from sub-Planckian components via the Kim-Nilles-Peloso alignment, with the outcome depending on $N_{ m axion}$ and $N_{ m source}$, producing either natural or multi-natural inflation. The authors quantify the likelihood of obtaining large $f_{ m eff}$, finding non-negligible probabilities that grow with $N_{ m axion}$, and discuss how short inflation can leave observable signatures such as negative spatial curvature. They also analyze reheating and leptogenesis, estimating a reheating temperature around $T_R\sim 4\times 10^{10}$ GeV and showing both thermal and non-thermal leptogenesis are viable within this framework. The axion landscape thus provides a UV-friendly avenue to realize large-field inflation, connect to string theory moduli, and yield testable cosmological signatures, including the scale of inflation and possible running of the spectral index.

Abstract

We propose a landscape of many axions, where the axion potential receives various contributions from shift symmetry breaking effects. We show that the existence of the axion with a super-Planckian decay constant is very common in the axion landscape for a wide range of numbers of axions and shift symmetry breaking terms, because of the accidental alignment of axions. The effective inflation model is either natural or multi-natural inflation in the axion landscape, depending on the number of axions and the shift symmetry breaking terms. The tension between BICEP2 and Planck could be due to small modulations to the inflaton potential or steepening of the potential along the heavy axions after the tunneling. The total duration of the slow-roll inflation our universe experienced is not significantly larger than $60$ if the typical height of the axion potentials is of order $(10^{16-17}{\rm \,GeV})^4$.

Figures (4)

• Figure 1: Illustration of the axion landscape. The landscape consists of many axions with sinusoidal potentials of various height and periodicity. There is likely to be a flat direction with an effective super-Planckian decay constant because of the accidental alignment of axions, whereas the typical curvature at the false vacua is much larger than the Hubble parameter. The inflaton is one of the lightest axions, and the natural or multi-natural inflation takes place after the last Coleman-De-Luccia tunneling event.
• Figure 2: The integrated probability distribution functions, ${\cal P}(f_{\rm eff}/f_i)$, for the lightest (solid), second lightest (dashed), and third lightest (dash dotted) mass eigenvalues, from right to left. We generated $10^5$ random matrices with $N_{\rm axion} = 10$ and $n=2$. The probability for the enhancement by more than $10^3$ is about $1\%$. It is rare that two (or three) flat directions arise simultaneously by the accidental alignment.
• Figure 3: The integrated probability distribution functions, ${\cal P}(f_{\rm eff}/f_i)$, for the case of $N_{\rm source} = N_{\rm axion}, N_{\rm axion}+1, N_{\rm axion}+2$, from right to left. We generated $10^5$ random matrices and set $N_{\rm axion} = 10$. As the number of shift symmetry breaking terms increases, it becomes more difficult to realize the suppression of the lightest mass eigenvalues (or equivalently, the enhancement of the decay constant).
• Figure 4: The probability to have a flat direction with the decay constant more than $10^2$ (upper), $10^3$ (middle), and $10^4$ (bottom) times larger than the typical value in one realization of the axion landscape, as a function of $N_{\rm axion} = N_{\rm source}$.