deletions | additions       diff --git a/reconstructed_wedges.tex b/reconstructed_wedges.tex  index af3a7c2..dae41ce 100644  --- a/reconstructed_wedges.tex  +++ b/reconstructed_wedges.tex 
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Figures \ref{fig:HDA_z60_epsilon0.15}-\ref{fig:HDA_z26_epsilon0.15} display results. In the 2D panels the even contour solid red lines are the 68, 95\% confidence level regions, and we add a Gaussian approximation in each panel based on the mode value, the median value of the 68\% CL region width and the covariance $r$ between the two parameters.   Due to limitations of the data to constrain the parameter space, here we present results with a prior of 15\% on $\epsilon$ ($\epsilon \sim 1/H/D_{\rm A}$).   To assess reasonable priors on $\epsilon$ due to observations, $\epsilon$,  we examine exmamine predicted results according to the Planck data (cite Planck). We analyze  propositions of MCMC obtained  when analyzing the using cosmomc (cite and explain cosmomc).   Fitting models to  Planck temperature anisotropies and examine predictions WMAP polarization (cite) we investigate predications  for $\alpha$ ($\alpha \sim D_{\rm A}^2/H$) and $\epsilon$ at our redshifts of interest ($0.44,0.6,0.73$). Assuming an $ow$CDM model, we obtain a 68\% CL region of $22\%$ for $\alpha$ and $\sim 2.5\%$ for $\epsilon$. Examining a more restrictive flat-$\Lambda$CDM model we find a 68\% CL region of $2\%$ for $\alpha$ and similar for $\epsilon$. We argue that the reason the $\alpha$ of Planck are sensitive to assumption of flatness and $w$ and $\epsilon$ is not is due to the capability of Planck to constrain $H_{\rm 0}$, which $\alpha$ is sensitive to, but $\epsilon$ is not. We clearly see that the 1$\sigma$ CL region engulfs the fiducial value use for analysis. The 2$\sigma$ region is ill-constrained.