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 $(10^{16-17}{\rm \,GeV})^4$.
Highlights
Observations of Planck and BICEP2, arXiv:1403.5277 [INSPIRE]. [24] M
We propose a landscape of many axions, where the axion potential receives various contributions from shift symmetry breaking effects
We have proposed a landscape of many axions where the axion potential receives various contributions from shift symmetry breaking effects
Summary
We must have a good control of the inflaton potential over more than about 10 times the reduced Planck scale for successful large-field inflation suggested by the BICEP2 result [1]. One way for realizing a sufficiently flat potential over large field ranges is to impose a shift symmetry on the inflaton:. Where f is the decay constant and Λ denotes a dynamically generated scale violating the continuous shift symmetry. Where θi denotes a relative phase between different sinusoidal functions and a constant term V0 is to make the cosmological constant vanish in the present vacuum. This is the multinatural inflation [6, 24, 25].2. In the multi-natural inflation, at least one of the decay constants must be greater than the Planck scale to explain the BICEP2 result, the lower bound on fi is relaxed compared to the natural inflation
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