Discerning dark energy models with high redshift standard candles

Following the success of type Ia supernovae in constraining cosmologies at lower redshift (z ≲ 2), effort has been spent determining if a similarly useful standardizable candle can be found at higher redshift. In this work, we determine the largest possible magnitude discrepancy between a constant dark energy ΛCDM 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 ≳ 2). We discuss a number of popular parametrizations of w(z) with two free parameters, wzCDM cosmologies, including the Chevallier-Polarski-Linder and generalization thereof, nCPL, as well as the Jassal-Bagla-Padmanabhan parametrization. For each of these parametrizations, we calculate and find the extrema of Δμ, the difference between the distance modulus of a wzCDM cosmology and a fiducial ΛCDM cosmology as a function of redshift, given 68 per cent likelihood constraints on the parameters P = (Ωm, 0, w0, wa). 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 ΛCDM cosmology at high redshift, implying that high redshift standard candles will not aid in discerning between the wzCDM cosmology and the fiducial ΛCDM cosmology. Conversely, this implies that if high redshift standard candles are found to be in disagreement with ΛCDM at high redshift, then this is a problem not only for ΛCDM but for the entire family of wzCDM cosmologies.