Reduction of Cosmological Data for the Detection of Time-varying Dark Energy Density

We present a method for reducing cosmological data to constraints on the amplitudes of modes of the dark energy density as a function of redshift. The modes are chosen so that 1) one of them has constant density and 2) the others are non-zero only if there is time-variation in the dark energy density and 3) the amplitude errors for the time-varying modes are uncorrelated with each other. We apply our method to various combinations of three-year WMAP data (Spergel et al., 2006), baryon acoustic oscillation data (Eisenstein et al., 2005), the Riess et al. (2004) ’Gold’ supernova data set, and the Supernova Legacy Survey data set (Astier et al., 2005). We find no significant evidence for a time-varying dark energy density or for non-zero mean curvature. Although by some measure the limits on four of the timevarying mode amplitudes are quite tight, they are consistent with the expectation that the dark energy density does not vary on time scales shorter than a Hubble time. Since we do not expect detectable time variation in these modes, our results should be viewed as a systematic error test which the data have passed. We discuss a procedure to identify modes with maximal signal-to-noise ratio. Subject headings: cosmology: theory – cosmology: observation