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.