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 40 h ^ { -1 } \mathrm { 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 \pm 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 .
) .