Observational implications of axionic isocurvature fluctuations

The axion is the most attractive candidate to solve the strong CP problem in QCD. If it exists, the inflationary universe produces axion fluctuations which are mixtures of isocurvature and adiabatic fluctuations in general. We investigate how large isocurvature fluctuations are allowed or favored in order to explain observations of the large scale structure of the present universe. Generic flat universe models with mixed (isocurvature + adiabatic) density fluctuations are studied. It is found that the observations are consistent with the mixed fluctuation model if the ratio alpha of the power spectrum of isocurvature fluctuations to that of adiabatic fluctuations is less than similar to 0.1. In particular, the mixed fluctuation model with alpha similar to 0.05, total matter density Omega(0) = 0.4, and Hubble parameter H-0 = 70 km/s/Mpc gives a very good fit to the observational data. Since the height of the acoustic peak in the angular power spectrum of the cosmic microwave background (CMB) radiation decreases significantly when the isocurvature fluctuations are present, the mixed fluctuation model can be tested in future satellite experiments. Ratios of the amplitude at the peak location to that at the COBE normalization scale for various models are given. Furthermore, we also obtain the amplitude of isocurvature fluctuations as a function of axion parameters and the Hubble parameter during the inflation. We discuss the axion fluctuations in some realistic inflation models and find that a significant amount of the isocurvature fluctuations are naturally produced.