Testing Lambda and the Limits of Cosmography with the Union2.1 Supernova
  Compilation
  We present a cosmographic study designed to test the simplest type of
accelerating cosmology: a flat universe with matter and a cosmological constant
($\Lambda$). Hubble series expansions are fit to the SCP Union2.1 supernova
data set to estimate the Hubble Constant ($H_{0}$), the deceleration parameter
($q_{0}$), and the jerk parameter ($j_{0}$). Flat $\Lambda$CDM models always
require $j_{0} = 1$, providing a single-parameter test of the entire paradigm.
Because of convergence issues for $z \gtrsim 1$, we focus on expansions using
the newer redshift variable $y$, and to estimate the effects of "model-building
uncertainties" -- the dependence of the output results upon the fitting
function and parameters used -- we perform fits using five different distance
indicator functions, and four different polynomial orders. We find that one
cannot yet use the supernova data to reliably obtain more than four
cosmological parameters, and that cosmographic estimates of $j_{0}$ remain
dominated by model-building uncertainties, in conjunction with statistical and
other error sources. While $j_{0} = 1$ remains consistent with Union2.1, the
most restrictive bound that we can place is $j_{0} \sim [-7.6,8.5]$. To test
the future prospects of cosmography with new standard candle data, ensembles of
mock supernova data sets are created, and it is found that the best way to
reduce model-building uncertainties on lower-order Hubble parameters (such as
$\{H_{0}, q_{0}, j_{0} \}$) is by limiting the redshift range of the data. Thus
more and better $z \lesssim 1$ data, not higher-redshift data, is needed to
sharpen cosmographic tests of flat $\Lambda$CDM.
