  One of the main science goals of the Large Synoptic Survey Telescope (LSST)
is to uncover the nature of cosmic acceleration. In the base analysis, possible
deviations from the Lambda-Cold-Dark-Matter ($\Lambda$CDM) background evolution
will be probed by fitting a $w(z)$CDM model, which allows for a
redshift-dependent dark energy equation of state with $w(z)$, within general
relativity (GR). A rich array of other phenomena can arise due to deviations
from the standard $\Lambda$CDM+GR model though, including modifications to the
growth rate of structure and lensing, and novel screening effects on non-linear
scales. Concrete physical models are needed to provide consistent predictions
for these (potentially small) effects, to give us the best chance of detecting
them and separating them from astrophysical systematics. A complex plethora of
possible models has been constructed over the past few decades, with none
emerging as a particular favorite. This document prioritizes a subset of these
models along with rationales for further study and inclusion into the LSST Dark
Energy Science Collaboration (DESC) data analysis pipelines, based on their
observational viability, theoretical plausibility, and level of theoretical
development. We provide references and theoretical expressions to aid the
integration of these models into DESC software and simulations, and give
justifications for why other models were not prioritized. While DESC efforts
are free to pursue other models, we provide here guidelines on which theories
appear to have higher priority for collaboration efforts due to their perceived
promise and greater instructional value.
