Recent work suggests that Type Ia supernovae (SNe) are composed of two distinct populations: prompt and delayed. By explicitly incorporating properties of host galaxies, it may be possible to target and eliminate systematic differences between these
two putative populations. However, any resulting {em post}-calibration shift in luminosity between the components will cause a redshift-dependent systematic shift in the Hubble diagram. Utilizing an existing sample of 192 SNe Ia, we find that the average luminosity difference between prompt and delayed SNe is constrained to be $(4.5 pm 8.9)%$. If the absolute difference between the two populations is 0.025 mag, and this is ignored when fitting for cosmological parameters, then the dark energy equation of state (EOS) determined from a sample of 2300 SNe Ia is biased at $sim1sigma$. By incorporating the possibility of a two-population systematic, this bias can be eliminated. However, assuming no prior on the strength of the two-population effect, the uncertainty in the best-fit EOS is increased by a factor of 2.5, when compared to the equivalent sample with no underlying two-population systematic. To avoid introducing a bias in the EOS parameters, or significantly degrading the measurement accuracy, it is necessary to control the post-calibration luminosity difference between prompt and delayed SN populations to better than 0.025 mag.
Our ignorance of the dark energy is generally described by a two-parameter equation of state. In these approaches a particular {it ad hoc} functional form is assumed, and only two independent parameters are incorporated. We propose a model-independen
t, multi-parameter approach to fitting the dark energy, and show that next-generation surveys will constrain the equation of state in three or more independent redshift bins to better than 10%. Future knowledge of the dark energy will surpass two numbers (e.g., [$w_0$,$w_1$] or [$w_0$,$w_a$]), and we propose a more flexible approach to the analysis of present and future data.
The gravitational magnification and demagnification of Type Ia supernovae (SNe) modify their positions on the Hubble diagram, shifting the distance estimates from the underlying luminosity-distance relation. This can introduce a systematic uncertaint
y in the dark energy equation of state (EOS) estimated from SNe, although this systematic is expected to average away for sufficiently large data sets. Using mock SN samples over the redshift range $0 < z leq 1.7$ we quantify the lensing bias. We find that the bias on the dark energy EOS is less than half a percent for large datasets ($gtrsim$ 2,000 SNe). However, if highly magnified events (SNe deviating by more than 2.5$sigma$) are systematically removed from the analysis, the bias increases to $sim$ 0.8%. Given that the EOS parameters measured from such a sample have a 1$sigma$ uncertainty of 10%, the systematic bias related to lensing in SN data out to $z sim 1.7$ can be safely ignored in future cosmological measurements.
