Cosmological constraints from the CMB and Ly-alpha forest revisited

The WMAP team has recently highlighted the usefulness of combining the Ly-alpha forest constraints with those from the cosmic microwave background (CMB). This combination is particularly powerful as a probe of the primordial shape of the power spectrum. Converting between the Ly-alpha forest observations and the linear mass power spectrum requires a careful treatment of nuisance parameters and modeling with cosmological simulations. We point out several issues which lead to an expansion of the errors, the two most important being the range of cosmological parameters explored in simulations and the treatment of the mean transmitted flux constraints. We employ a likelihood calculator for the current Ly-alpha data set based on an extensive 6-dimensional grid of simulations. We show that the current uncertainties in the mean transmission and the flux power spectrum define a degeneracy line in the amplitude-slope plane. The CMB degeneracy due to the primordial power spectrum shape follows a similar relation in this plane. This weakens the statistical significance of the primordial power spectrum shape constraints based on combined CMB+Ly-alpha forest analysis. Using the current data the simplest n=1 scale invariant model with dn/dln k=0 and no tensors has a Delta chi^2=4 compared to the best fitting model in which these 3 parameters are free. Current data therefore do not require relaxing these parameters to improve the fit.