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.
