Reduction of cosmological data for the detection of time-varying dark energydensity

Abstract

We present a method for reducing cosmological data to constraints on the amplitudes ofmodes of the dark energy density as a function of redshift. The modes are chosenso that (1) one of them has constant density and (2) the others are non-zeroonly if there is time-variation in the dark energy density and (3) the amplitudeerrors for the time-varying modes are uncorrelated with each other. We applyour method to various combinations of three-year WMAP data, baryon acousticoscillation data, the ‘Gold’ supernova data set, and the Supernova Legacy Survey dataset. We find no significant evidence for a time-varying dark energy density orfor non-zero mean curvature. Although by some measure the limits on four ofthe time-varying mode amplitudes are quite tight, they are consistent with theexpectation that the dark energy density does not vary on timescales shorter than aHubble time. Since we do not expect detectable time variation in these modes, ourresults 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.