The Essence of Quintessence and the Cost of Compression

Standard two-parameter compressions of the infinite dimensional dark energymodel space show crippling limitations even with current SN-Ia data. Firstlythey cannot cope with rapid evolution - the best-fit to the latest SN-Ia datashows late and very rapid evolution to w_0 = -2.85. However all of the standardparametrisations (incorrectly) claim that this best-fit is ruled out at morethan 2-sigma, primarily because they track it well only at very low redshifts,z < 0.2. Further they incorrectly rule out the observationally acceptableregion w << -1 for z > 1. Secondly the parametrisations give wildly differentestimates for the redshift of acceleration, which vary from z_{acc}=0.14 toz_{acc}=0.59. Although these failings are largely cured by includinghigher-order terms (3 or 4 parameters) this results in new degeneracies whichopen up large regions of previously ruled-out parameter space. Finally we testthe parametrisations against a suite of theoretical quintessence models. Thewidely used linear expansion in z is generally the worst, with errors of up to10% at z=1 and 20% at z > 2. All of this casts serious doubt on the usefulnessof the standard two-parameter compressions in the coming era of high-precisiondark energy cosmology and emphasises the need for decorrelated compressionswith at least three parameters.Comment: 7 pages, 4 colour figures, EmulateApJ; v2: includes Bayesian evidence analysis and table that were only present in published version, because of increased interest in Bayesian model comparison (no new material beyond the one in the published ApJL of 2004