Fisher matrix for multiple tracers: all you can learn from large-scale
  structure without assuming a model
  The galaxy power spectrum is one of the central quantities in cosmology. It
contains information about the primordial inflationary process, the matter
clustering, the baryon-photon interaction, the effects of gravity, the
galaxy-matter bias, the cosmic expansion, the peculiar velocity field, etc..
Most of this information is however difficult to extract without assuming a
specific cosmological model, for instance $\Lambda$CDM and standard gravity. In
this paper we explore instead how much information can be obtained that is
independent of the cosmological model, both at background and linear
perturbation level. We determine the full set of model-independent statistics
that can be constructed by combining two redshift bins and two distinct
tracers. We focus in particular on the statistics $r(k,z_1,z_2)$, defined as
the ratio of $f\sigma_8(z)$ at two redshift shells, and we show how to estimate
it with a Fisher matrix approach. Finally, we forecast the constraints on $r$
that can be achieved by future galaxy surveys, and compare it with the standard
single-tracer result. We find that $r$ can be measured with a precision from 3
to 11%, depending on the survey. Using two tracers, we find improvements in the
constraints up to a factor of two.
