Peculiar velocity cosmology with type Ia supernovae
  Type Ia Supernovae have yet again the opportunity to revolutionize the field
of cosmology as the new generation of surveys are acquiring thousands of nearby
SNeIa opening a new era in cosmology: the direct measurement of the growth of
structure parametrized by $fD$. This method is based on the SNeIa peculiar
velocities derived from the residual to the Hubble law as direct tracers of the
full gravitational potential caused by large scale structure. With this
technique, we could probe not only the properties of dark energy, but also the
laws of gravity. In this paper we present the analytical framework and
forecasts. We show that ZTF and LSST will be able to reach 5\% precision on
$fD$ by 2027. Our analysis is not significantly sensitive to photo-typing, but
known selection functions and spectroscopic redshifts are mandatory. We finally
introduce an idea of a dedicated spectrograph that would get all the required
information in addition to boost the efficiency to each SNeIa so that we could
reach the 5\% precision within the first two years of LSST operation and the
few percent level by the end of the survey.
