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 rms fluctuation amplitude of matter fluctuations is \sigma _ { 8 } = 0.94 \pm 0.08 and { \mbox { n$ { } _ { s } $ } } = 0.99 \pm 0.03 , if we do not include running of the spectral index .
The best fit model with a running spectral index has parameters { \mbox { n$ { } _ { s } $ } } = 0.959 \pm 0.036 and { \mbox { n$ { } _ { run } $ } } = -0.033 \pm 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 .