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Relativistic corrections and non-Gaussianity in radio continuum surveys

Forthcoming radio continuum surveys will cover large volumes of the observable Universe and will reach to high redshifts, making them potentially powerful probes of dark energy, modified gravity and non-Gaussianity. Here we extend recent works by analyzing the general relativistic (GR) corrections to the angular power spectrum. These GR corrections to the standard Newtonian analysis of the power spectrum become significant on scales near and beyond the Hubble scale at each redshift. We consider the continuum surveys with LOFAR, WSRT and ASKAP, and examples of continuum surveys with the SKA. We find that the GR corrections are at most percent-level in LOFAR, WODAN and EMU surveys, but they can produce $O(10%)$ changes for high enough sensitivity SKA continuum surveys. The signal is however dominated by cosmic variance, and multiple-tracer observations will be needed to overcome this problem. The GR corrections are suppressed in continuum surveys because of the integration over redshift -- we expect that GR corrections will be enhanced for future SKA HI surveys in which the source redshifts will be known. We also provide predictions for the angular power spectra in the case where the primordial perturbations have local non-Gaussianity. We find that non-Gaussianity dominates over GR corrections, and rises above cosmic variance when $f_{\rm NL}\gtrsim5$ for SKA continuum surveys.