Domain Wall Problem of Axion and Isocurvature Fluctuations in Chaotic Inflation Models

We study the domain wall problem of an axion in chaotic inflation models. We show that the production of domain walls does not occurs if the PecceiQuinn scalar has a flat potential and its breaking Fa is larger than ∼ 10GeV. We find that too large isocurvature fluctuations are produced for such high Fa. In order for those isocurvature fluctuations to be consistent with observations of the large scale structure of the universe, the self-coupling constant g and the breaking scale of the Peccei-Quinn scalar should be g ≃ (1− 2.8)× 10 and Fa ≃ (0.6 − 1.5) × 10GeV, respectively. In particular the value of selfcoupling constant is almost the same as that required for a chaotic inflation, which strongly suggests that the Peccei-Quinn scalar itself is an inflaton. PACS: 14.80.MZ, 95.35.+d, 98.65.-r, 98.70.Vc, 98.80.-k, 98.80.Cq, 98.80.Es The axion [1, 2, 3, 4] is the most natural solution to the strong CP problem in QCD [5]. The axion is associated with breaking of the Peccei-Quinn symmetry whose breaking scale Fa is stringently constrained by laboratory experiments, astrophysics and cosmology; the allowed range of Fa is between 10 10 GeV and 10 GeV [6] in the standard cosmology. The lower limit comes from consideration of the cooling of the supernova SN1987A by axions and the upperbound is obtained by requiring the the cosmic axion density should not exceed the critical density of the universe. Thus the axion is one of attractive candidates for dark matter if Fa takes higher values in the allowed region. However, in the standard cosmology the axion has a domain-wall problem [7]. Since the potential of the axion which is formed through QCD instanton effects has N discrete minima ( N : color anomaly factor), domain walls are produced at the QCD scale. The domain walls with N > 1 form very complicated network together with axionic strings which are produced associated with spontaneous breaking of Peccei-Quinn symmetry and do not disappear in the subsequent evolution of the universe, which leads to a cosmological disaster. In the inflationary universe [8, 9] it is generally expected that the domain wall problem is solved since the exponential expansion during inflation makes the phase of Peccei-Quinn scalar (=axion) homogeneous beyond the present horizon of the universe and hence axions settle down to the same minimum of the potential in the entire universe. However, in the chaotic inflationary universe [10] the domain walls are produced through large quantum fluctuations of axions generated in the chaotic inflation [11]. The quantum fluctuations of axions δa are given by H/(2π) where H is the Hubble constant during inflation. δa is 10GeV for chaotic inflation and it is larger than the Peccei-Quinn scale Fa. This means that the axion phases θa ≡ a/Fa become random after inflation and domain walls are produced in the same way as the standard cosmology. The domain walls with N = 1 have disk-like structure whose boundaries are axionic strings, and they collapse and disappear so rapidly that they are cosmologically harmless.