Observational Implications of Axionic Isocurvature Fluctuations

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 mixture 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 the mixed (isocurvature + adiabatic) density fluctuations are studied. It is found that the observations are consistent with the mixed fluctuation model if ratio $\alpha$ of the power spectrum of isocurvature fluctuations to that of adiabatic fluctuations is less than $\sim 0.1$. In particular, the mixed fluctuation model with $\alpha \sim 0.05$, total matter density $\Omega =0.4$ 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 the one at the COBE normalization scale for various models are shown. 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 a hybrid inflation model and find that a significant amount of the isocurvature fluctuations are produced if the axion decay constant $F_{a} \simeq 10^{15}-10^{16}$GeV. We also briefly discuss a possible connection with the M-theory axion model.