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Constraints on CDM cosmology from galaxy power spectrum, CMB and SNIa evolution

We examine the constraints that can be obtained on standard cold dark matter models from the most currently used data set: CMB anisotropies, type Ia supernovae and the SDSS luminous red galaxies. We also examine how these constraints are widened when the equation of state parameter $w$ and the curvature parameter $Ω_k$ are left as free parameters. For the $Λ$CDM model, our 'vanilla' model, cosmological parameters are tightly constrained and consistent with current estimates from various methods. When the dark energy parameter $w$ is free we find that the constraints remain mostly unchanged, i.e. changes are smaller than the 1 sigma uncertainties. Similarly, relaxing the assumption of a flat universe leads to nearly identical constraints on the dark energy density parameter of the universe $Ω_Λ$, baryon density of the universe $Ω_b $, the optical depth $τ$, the index of the power spectrum of primordial fluctuations $n_S$, with most one sigma uncertainties better than 5%. More significant changes appear on other parameters: while preferred values are almost unchanged, uncertainties for the physical dark matter density $Ω_ch^2$, Hubble constant $H_0$ and $σ_8$ are typically twice as large. We found that different methodological approaches on large scale structure estimates lead to appreciable differences in preferred values and uncertainty widths. We also found that possible evolution in SNIa intrinsic luminosity does not alter these constraints by much, except for $w$, for which the uncertainty is twice as large. At the same time, this possible evolution is severely constrained. We conclude that systematic uncertainties for some estimated quantities are similar or larger than statistical ones.