A new way to test the Cosmological Principle: measuring our peculiar
  velocity and the large scale anisotropy independently
  We present a novel approach to disentangle two key contributions to the
largest-scale anisotropy of the galaxy distribution: (i) the intrinsic dipole
due to clustering and anisotropic geometry, and (ii) the kinematic dipole due
to our peculiar velocity. Including the redshift and angular size of galaxies,
in addition to their fluxes and positions allows us to measure both the
direction and amplitude of our velocity independently of the intrinsic dipole
of the source distribution. We find that this new approach applied to future
galaxy surveys (LSST and Euclid) and a SKA radio continuum survey will allow to
measure our velocity ($\beta = v/c$) with a relative error in the amplitude
$\sigma(\beta)/\beta \sim (1.3 - 4.5)\%$ and in direction, $\theta_{\beta} \sim
0.9^\circ - 3.9^\circ$, well beyond what can be achieved when analysing only
the number count dipole. We also find that galaxy surveys are able to measure
the intrinsic large-scale anisotropy with a relative uncertainty of $\lesssim
5\%$ (measurement error, not including cosmic variance). Our method enables two
simultaneous tests of the Cosmological Principle: comparing the observations of
our peculiar velocity with the CMB dipole, and testing for a significant
intrinsic anisotropy on large scales which would indicate effects beyond the
standard cosmological model.
