The 6x2pt method: supernova velocities meet multiple tracers
  We present a new methodology to analyse in a comprehensive way large-scale
and supernovae (or any other distance indicator) surveys. Our approach combines
galaxy and supernova position and redshift data with supernova peculiar
velocities, obtained through their magnitude scatter, to construct a 6x2pt
analysis which includes six power spectra. The 3x3 correlation matrix of these
spectra expresses exhaustively the information content of the surveys at the
linear level. We proceed then to forecast the performance of future surveys
like LSST and 4MOST with a Fisher Matrix analysis, adopting both a
model-dependent and a model-independent approach. We compare the performance of
the 6x2pt approach to the traditional one using only galaxy clustering and some
recently proposed combinations of galaxy and supernovae data and quantify the
possible gains by optimally extracting the linear information. We show that the
6x2pt method shrinks the uncertainty area in the $\sigma_8, \gamma$ plane by
more than half when compared to the traditional method. The combined clustering
and velocity data on the growth of structures has uncertainties at similar
levels to those of the CMB but exhibit orthogonal degeneracies, and the
combined constraints yield improvements of factors of 5 in each of the five
cosmological parameters here considered. Concerning the model-independent
results, we find that our method can improve the constraints on $H(z)/H_0$ in
all redshift bins by more than 70% with respect to the galaxy clustering alone
and by 30% when supernova velocities (but not clustering) are considered,
reaching a precision of 3-4% at high redshifts.
