Supernova surveys have played a crucial role in modern cosmology. It is with these surveys that we can most directly measure the overall expansion rate of the Universe, also known as the “Hubble flow.” Indeed, the 2011 Nobel Prize in Physics went to the first teams to use this technique to determine that the expansion of the Universe is mysteriously speeding up with time.
This method rests on our ability to infer the intrinsic brightnesses of Type Ia supernovae and then compare them with the measured fluxes to obtain distances. Put simply, the farther away an object is, the dimmer it appears. We can also measure distance with redshifts — since the Universe is expanding, any light that travels to us gets stretched. The farther away an object is, the more time the light has to stretch, and the more reddening that we see.
The resulting data set is translated into cosmological knowledge by fitting what we see to the predictions from cosmological models. The models are typically assumed to have a uniform, homogeneous density distribution. But the Universe is actually clumpy on small scales, and Doppler Shift errors arise from neglected motions with respect to the overall Hubble flow. These motions are due to the gravity-fueled growth of cosmic structures, and they are difficult to calculate theoretically because structure growth is a highly nonlinear process.
We can probe structure growth with numerical simulations such as the large-scale Millennium Simulation. I performed mock supernova surveys within this simulation volume to ask how does ignoring the extra motion induced by the clumpiness of the Universe impact our ability to measure its properties with supernovae?
This analysis required thousands of Monte-Carlo runs to build up good statistics. I was eventually able to model the behavior of the resulting error as a function of survey size and depth. Dealing with simulation data was computationally expensive; for each run I subdivided the available galaxy sample into smaller random subsamples to ease the memory load.
I found that the error for future deep supernova surveys is small when compared with the errors associated with our ignorance of intrinsic brightnesses, and provided useful fitting formulae.
Vanderveld (2008). Published in The Astrophysical Journal.