A combined analysis of Cosmic Microwave Background ( CMB ) and Lyman- \alpha forest data can constrain the matter power spectrum from small scales of about 1 h ^ { -1 } Mpc all the way to the horizon scale .
The long lever arm and complementarity provided by such an analysis has previously led to a significant tightening of the constraints on the shape and the amplitude of the power spectrum of primordial density fluctuations .
We present here a combined analysis of the WMAP three year results with Lyman- \alpha forest data .
The amplitude of the matter power spectrum \sigma _ { 8 } and the spectral index n _ { s } inferred from the joint analysis of high and low resolution Lyman- \alpha forest data as analysed by Viel & Haehnelt ( 34 ) are consistent with the new WMAP results to within 1 \sigma .
The joint analysis with the mainly low resolution data as analysed by McDonald et al .
( 20 ) suggest a value of \sigma _ { 8 } that is \sim 2 \sigma higher than that inferred from the WMAP three year data alone .
The joint analysis of the three year WMAP and the Lyman- \alpha forest data also does not favour a running of the spectral index .
The best fit values for a combined analysis of the three year WMAP data , other CMB data , 2dF and the Lyman- \alpha forest data are ( \sigma _ { 8 } , { \mbox { { \it n } $ { } _ { s } $ } } ) = ( 0.78 \pm 0.03 , 0.96 \pm 0.01 ) .