  The combined analysis of the cosmic microwave background on large scales and
Lyman-alpha forest on small scales provides a sufficiently long lever arm to
obtain strong constraints on the slope and curvature of the power spectrum of
primordial density fluctuations. We present results from the combination of the
first year WMAP data and the dark matter power spectrum inferred by Viel et al.
(2004) for two different sets of high resolution and high signal-to-noise
quasar absorption spectra: the Croft et al. (2002) sample with a median
redshift z=2.72 and the LUQAS sample (Kim et al. 2004) with a median redshift
z=2.125. The best fit value for the {\it rms} fluctuation amplitude of matter
fluctuations is sigma_8 =0.94 +- 0.08 and n=0.99 +- 0.03, if we do not include
running of the spectral index. The best fit model with a running spectral index
has parameters n=0.959 +- 0.036 and n_run=-0.033 +- 0.025. The data is thus
consistent with a scale-free primordial power spectrum with no running of the
spectral index. We further include tensor modes and constrain the slow-roll
parameters of inflation.
