Squeezing the window on isocurvature modes with the Lyman-α forest

Various recent studies proved that cosmological models with a significant contribution from cold dark matter isocurvature perturbations are still compatible with most recent data on cosmic microwave background anisotropies and on the shape of the galaxy power spectrum, provided that one allows for a very blue spectrum of primordial entropy fluctuations (n(iso)> 2). However, such models predict an excess of matter fluctuations on small scales, typically below 40h(-1) Mpc. We show that the proper inclusion of high-resolution high signal-to-noise Lyman-alpha forest data excludes most of these models. The upper bound on the isocurvature fraction alpha=f(iso)(2)/(1+f(iso)(2)), defined at the pivot scale k(0)=0.05 Mpc(-1), is pushed down to alpha < 0.4, while n(iso)=1.9 +/- 1.0 (95% confidence limits). We also study the bounds on curvaton models characterized by maximal correlation between curvature and isocurvature modes, and a unique spectral tilt for both. We find that f(iso)< 0.05 (95% C.L.) in that case. For double-inflation models with two massive inflatons coupled only gravitationally, the mass ratio should obey R < 3 (95% C.L.).