We present a Fourier analysis of the clustering of galaxies in the combined Main galaxy and Luminous Red Galaxy (LRG) Sloan Digital Sky Survey (SDSS) Data Release 5 (DR5) sample. The aim of our analysis is to consider how well we can measure the cosmological matter density using the signature of the horizon at matter-radiation equality embedded in the large-scale power spectrum. The new data constrains the power spectrum on scales 100--600h^-1Mpc with significantly higher precision than previous analyses of just the SDSS Main galaxies, due to our larger sample and the inclusion of the LRGs. This improvement means that we can now reveal a discrepancy between the shape of the measured power and linear CDM models on scales 0.01<k<0.15hMpc^-1, with linear model fits favouring a lower matter density (Omega_m=0.22+/-0.04) on scales 0.01<k<0.06hMpc^-1 and a higher matter density (Omega_m=0.32+/-0.01) when smaller scales are included, assuming a flat LCDM model with h=0.73 and n_s=0.96. This discrepancy could be explained by scale-dependent bias and, by analysing subsamples of galaxies, we find that the ratio of small-scale to large-scale power increases with galaxy luminosity, so all of the SDSS galaxies cannot trace the same power spectrum shape over 0.01<k<0.2hMpc^-1. However, the data are insufficient to clearly show a luminosity-dependent change in the largest scale at which a significant increase in clustering is observed, although they do not rule out such an effect. Significant scale-dependent galaxy bias on large-scales, which changes with the r-band luminosity of the galaxies, could potentially explain differences in our Omega_m estimates and differences previously observed between 2dFGRS and SDSS power spectra and the resulting parameter constraints.
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