Abstract
If the Peccei–Quinn symmetry is already broken during inflation, the decay constant Fa of the axion can be in a wide region from 1011GeV to 1018GeV for the axion being the dominant dark matter. In this case, however, the axion causes the serious cosmological problem, isocurvature perturbation problem, which severely constrains the Hubble parameter during inflation. The constraint is relaxed when Peccei–Quinn scalar field takes a large value ∼Mp (Planck scale) during inflation. In this letter, we point out that the allowed region of the decay constant Fa is reduced to a rather narrow region for a given tensor-to-scalar ratio r when Peccei–Quinn scalar field takes ∼Mp during inflation. For example, if the ratio r is determined as r≳10−3 in future measurements, we can predict Fa≃(0.1–1.4)×1012GeV for domain wall number NDW=6.
Highlights
The QCD axion [1, 2, 3, 4, 5] predicted in the Peccei-Quinn(PQ) mechanism [6, 7] is very interesting, since it solves the strong CP problem in QCD, and provides the dark matter density in the present universe [8, 9, 10]
We have studied the axion dark matter hypothesis and derived constraints on the axion decay constant Fa and the tensor-to-scalar ratio r from consideration of the axion isocurvature perturbations
In deriving the constraints we have assumed that the PQ scalar has a large expectation value ∼ Mp during inflation, otherwise we have severer constraints and almost all region of Fa is excluded for r 10−3 [see Eq (10)]
Summary
The QCD axion [1, 2, 3, 4, 5] predicted in the Peccei-Quinn(PQ) mechanism [6, 7] is very interesting, since it solves the strong CP problem in QCD, and provides the dark matter density in the present universe [8, 9, 10]. If the PQ symmetry is already broken during inflation, it is known that Fa can take a large region from 1011 GeV to 1018 GeV In this case, the axion field acquires quantum fluctuations with amplitude Hinf/2π (Hinf : the Hubble parameter during inflation), which result in isocurvature perturbations of the cold dark matter (CDM) [14, 15, 16, 17, 18]. Since the isocurvature perturbations are stringently constrained by observations of the cosmic microwave background (CMB) [19], Hinf should be very small, e.g. Hinf 108 GeV This problem is relaxed when the PQ field takes a large value like Planck scale (Mp) during inflation as first Linde pointed out [20].
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