Parameters and pitfalls in dark energy models with time varying equation of state

Are geometrical summaries of the CMB and LSS sufficient for estimating cosmological parameters? And how does our choice of a dark energy model impact the current constraints on standard cosmological parameters? We address these questions in the context of the widely used CPL parametrization of a time varying equation of state w in a cosmology allowing spatial curvature. We study examples of different behavior allowed in a CPL parametrization in a phase diagram, and relate these to effects on the observables. We examine parameter constraints in such a cosmology by combining WMAP5, SDSS, SNe, HST data sets by comparing the power spectra. We carefully quantify the differences of these constraints to those obtained by using geometrical summaries for the same data sets. We find that (a) using summary parameters instead of the full data sets give parameter constraints that are similar, but with discernible differences, (b) due to degeneracies, the constraints on the standard parameters broaden significantly for the same data sets. In particular, we find that in the context of CPL dark energy, (i) a Harrison-Zeldovich spectrum cannot be ruled out at $2\sigma$ levels with our current data sets. and (ii) the SNe IA, HST, and WMAP 5 data are not sufficient to constrain spatial curvature; we additionally require the SDSS DR4 data to achieve this.