Fluctuations of differential number counts of radio continuum sources

We investigate the differential number counts of sources in radio continuum surveys, including all terms at linear order in cosmological perturbations. Our framework does not assume a specific gauge condition. This general approach allows us to recover gauge invariance explicitly. With the complete derivations of the covariant volume integral on the past light cone, we have identified several contributions in the number counts. To clarify their underlying physics, we present each contribution in terms of scalar, vector and tensor modes. This theoretical framework promises to be widely applicable to continuum radio galaxy surveys to model the expected angular power spectrum and two-point correlation.