Breaking the Degeneracy of Cosmological Parameters in Galaxy Redshift Surveys

Abstract

The measurement of cosmological parameters is investigated in a representation of the least-action method that uses a redshift-space dataset to simultaneously constrain the real-space fields $\delta$,$\b v$. This method is robust in recovering the entire evolution of the matter density contrast and peculiar velocities of galaxies in real space from current galaxy redshift surveys. The main strength of the method is that it permits us to break the degeneracy of the parameters $b$ and $\Omegam$ (customarily measured in the ratio $\beta\equiv \Omegam^{0.6}/b$ from redshift-space distortions), and these are evaluated in the current context separately. The procedure provides a simple numerical means to extract as much information as possible from a given sample, in the simplest linear bias model, before resorting to cosmic complementarity to resolve the degeneracy in the measurement of $\Omegam$. The same premise applies to more sophisticated choices of bias models. We construct a likelihood parameter $\lambda(b,\Omegam)$ to evaluate the relative likelihood of different values of $b$ and $\Omegam$. The method is applied to the \iras redshift survey with a low-resolution Gaussian smoothing length of 1200 \km within a spherical region $x_{\rm max} \sim 15,000$ \km and the reconstructed velocity field is then compared with POTENT-reconstructed velocities from the Mark III radial-velocity dataset within a radius $\sim 5000$ \km, which have been suitably prepared to account for Malmquist bias and other systematic errors. The analysis yields a likelihood for the parameters that is overall consistent with $\Omegam\approx 0.3$ and $b\approx 1.1$, thus lending support to a non-vanishing cosmological constant $\Omega_{\Lambda}\approx 0.7$ in a flat universe.