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.