Jon Thaler tra. 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 2σ 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. We then use large scale structure data that will be available in the future in a nonstandard way to forecast the constraints on the dark energy equation of state. We argue that the shapes of cosmic voids, as measured in spectroscopic galaxy redshift surveys, constitute a promising new probe of dark energy (DE). We do this by forecasting constraints on the DE equation of state and its variation from current and future surveys and find that the promise of void shape measurements compares favorably to that of standard methods such as supernovae and cluster counts even for currently available data. Owing to the complementar
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