Abstract
We show that the initial misalignment angle of the QCD axion (or axion-like particles) can be set very close to π, if the QCD axion has a mixing with another heavy axion which induces the phase shift ≈ π after inflation. In the simplest case, the heavy axion plays the role of the inflaton, and we call such inflation as “πnflation”. The basic idea was first proposed by Daido and the present authors in ref. [1] in 2017 and more recently discussed in ref. [2]. We show that the QCD axion with a decay constant fa ≳ 3 × 109 GeV can explain dark matter by the πnflation mechanism. A large fraction of the parameter region has an overlap with the projected sensitivity of ORGAN, MADMAX, TOORAD and IAXO. We also study implications for the effective neutrino species and isocurvature perturbations. The πnflation can provide an initial condition for the hilltop inflation in the axion landscape, and in a certain set-up, a chain of the hilltop inflation may take place.
Highlights
-called classical axion window, fa 1012 GeV
We show that the initial misalignment angle of the QCD axion can be set very close to π, if the QCD axion has a mixing with another heavy axion which induces the phase shift ≈ π after inflation
If the inflaton has a mixing with the QCD axion,5 the sign of the QCD axion potential is flipped by the phase shift of π due to the inflaton dynamics
Summary
We explain the basic idea of the πnflation and its implications for the QCD axion abundance and isocurvature perturbations. The other thing is that the QCD axion a and the inflaton φ are not the mass eigenstates, in general In this case one has to take account of the mixing between them to follow their evolution during inflation. The mixing between φ and a is small both during inflation and in the low energy, but the inflaton dynamics does contribute to the effective strong CP phase and shifts the potential minimum of a [1, 2]. We define πnflation such that the field evolution of the inflaton (i.e. πnflaton) gives a phase shift close to π (mod 2π) for another axion through mixing In our case, this is equivalent to nmix (φmin − fφ φinf ). We do not consider the contribution of the stochastic dynamics of φ to δ in the following
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