Constraints on the Primordial Power Spectrum from High Resolution Lyman-alpha Forest Spectra and WMAP

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.