We measured the harmonic-space power spectrum of Galaxy clustering auto-correlation from the Evolutionary Map of the Universe Pilot Survey 1 data (EMU PS1) and its cross-correlation with the lensing convergence map of cosmic microwave background (CMB) from Planck Public Release 4 at the linear scale range from $\ell=2$ to 500. We applied two flux density cuts at $0.18$ and $0.4$ mJy on the radio galaxies observed at 944MHz and considered two source detection algorithms. We found the auto-correlation measurements from the two algorithms at the 0.18 mJy cut to deviate for $\ell\gtrsim250$ due to the different criteria assumed on the source detection and decided to ignore data above this scale. We report a cross-correlation detection of EMU PS1 with CMB lensing at $\sim$5.5$\sigma$, irrespective of flux density cut. In our theoretical modelling we considered the SKADS and T-RECS redshift distribution simulation models that yield consistent results, a linear and a non-linear matter power spectrum, and two linear galaxy bias models. That is a constant redshift-independent galaxy bias $b(z)=b_g$ and a constant amplitude galaxy bias $b(z)=b_g/D(z)$. By fixing a cosmology model and considering a non-linear matter power spectrum with SKADS, we measured a constant galaxy bias at $0.18$ mJy ($0.4$ mJy) with $b_g=2.32^{+0.41}_{-0.33}$ ($2.18^{+0.17}_{-0.25}$) and a constant amplitude bias with $b_g=1.72^{+0.31}_{-0.21}$ ($1.78^{+0.22}_{-0.15}$). When $\sigma_8$ is a free parameter for the same models at $0.18$ mJy ($0.4$ mJy) with the constant model we found $\sigma_8=0.68^{+0.16}_{-0.14}$ ($0.82\pm0.10$), while with the constant amplitude model we measured $\sigma_8=0.61^{+0.18}_{-0.20}$ ($0.78^{+0.11}_{-0.09}$), respectively. Our results agree at $1\sigma$ with the measurements from Planck CMB and the weak lensing surveys and also show the potential of cosmology studies with future radio continuum survey data.

The angular power spectrum is a natural tool to analyse the observed galaxy number count fluctuations. In a standard analysis, the angular galaxy distribution is sliced into concentric redshift bins and all correlations of its harmonic coefficients between bin pairs are considered—a procedure referred to as ‘tomography’. However, the unparalleled quality of data from oncoming spectroscopic galaxy surveys for cosmology will render this method computationally unfeasible, given the increasing number of bins. Here, we put to test against synthetic data a novel method proposed in a previous study to save computational time. According to this method, the whole galaxy redshift distribution is subdivided into thick bins, neglecting the cross-bin correlations among them; each of the thick bin is, however, further subdivided into thinner bins, considering in this case all the cross-bin correlations. We create a simulated data set that we then analyse in a Bayesian framework. We confirm that the newly proposed method saves computational time and gives results that surpass those of the standard approach.