Discerning Dark Energy Models with High-Redshift Standard Candles
  Following the success of type Ia supernovae in constraining cosmologies at
lower redshift $(z\lesssim2)$, effort has been spent determining if a similarly
useful standardisable candle can be found at higher redshift. {In this work we
determine the largest possible magnitude discrepancy between a constant dark
energy $\Lambda$CDM cosmology and a cosmology in which the equation of state
$w(z)$ of dark energy is a function of redshift for high redshift standard
candles $(z\gtrsim2)$}. We discuss a number of popular parametrisations of
$w(z)$ with two free parameters, $w_z$CDM cosmologies, including the
Chevallier-Polarski-Linder and generalisation thereof, $n$CPL, as well as the
Jassal-Bagla-Padmanabhan parametrisation. For each of these parametrisations we
calculate and find extrema of $\Delta \mu$, the difference between the distance
modulus of a $w_z$CDM cosmology and a fiducial $\Lambda$CDM cosmology as a
function of redshift, given 68\% likelihood constraints on the parameters
$P=(\Omega_{m,0}, w_0, w_a)$. The parameters are constrained using cosmic
microwave background, baryon acoustic oscillations, and type Ia supernovae data
using CosmoMC. We find that none of the tested cosmologies can deviate more
than 0.05 mag from the fiducial $\Lambda$CDM cosmology at high redshift,
implying that high redshift standard candles will not aid in discerning between
a $w_z$CDM cosmology and the fiducial $\Lambda$CDM cosmology. Conversely, this
implies that if high redshift standard candles are found to be in disagreement
with $\Lambda$CDM at high redshift, then this is a problem not only for
$\Lambda$CDM but for the entire family of $w_z$CDM cosmologies.
