Scale dependence of the primordial spectrum from combining the three-year WMAP, galaxy clustering, supernovae, and Lyman-alpha forests

We probe the scale dependence of the primordial spectrum in the light of the three-year WMAP (WMAP3) alone and WMAP3 in combination with the other cosmological observations such as galaxy clustering and type Ia supernova (SNIa). We pay particular attention to the combination with the Lyman-alpha (Ly alpha) forest. In contrast to the first-year WMAP (WMAP1), WMAP3's preference for the running of the scalar spectral index on large scales is now fairly independent of the low CMB multipoles l. A combination with the galaxy power spectrum from the Sloan Digital Sky Survey (SDSS) prefers a negative running to larger than 2 sigma, regardless of the presence of the low-l CMB ( 2 <= l <= 23) or not. On the other hand, if we focus on the power law Lambda CDM cosmology with only six parameters (matter density Omega(m)h(2), baryon density Omega(b)h(2), Hubble constant H-0, optical depth tau, the spectral index, ns, and the amplitude, A(s), of the scalar perturbation spectrum) when we drop the low-l CMB contributions WMAP3 is consistent with the Harrison-Zel'dovich-Peebles scale-invariant spectrum (n(s) = 1 and no tensor contributions) at similar to 1 sigma. When assuming a simple power-law primordial spectral index or a constant running, in the case when one drops the low-l contributions ( 2 <= l <= 23) WMAP3 is more consistent with the other observations, such as the inferred value of sigma(8).