  Following on our purpose of developing a unified pipeline for large-scale
structure data analysis with angular (i.e. harmonic-space) power spectra, we
now include the weak lensing effect of magnification bias on galaxy clustering
in a publicly available, modular parameter estimation code. We thus forecast
constraints on the parameters of the concordance cosmological model, dark
energy, and modified gravity theories from galaxy clustering tomographic
angular power spectra. We find that a correct modelling of magnification is
crucial in order not to bias the estimation of cosmological parameters,
especially in the case of deep galaxy surveys. Our case study adopts
specifications of the Evolutionary Map of the Universe (EMU), which is a
full-sky, deep radio-continuum survey, and is expected to probe the Universe up
to redshift $z\sim6$. We assume the Limber approximation, and include
magnification bias on top of density fluctuations and redshift-space
distortions. By restricting our analysis to the regime where the Limber
approximation holds true, we significantly minimise the computational time
needed, compared to that of the exact calculation. We also show that there is a
trend for more biased parameter estimates from neglecting magnification when
the redshift bins are very wide. We conclude that this result implies a strong
dependence on the lensing contribution, which is an integrated effect and
becomes dominant when wide redshift bins are considered. Finally, we note that
instead of being considered a contaminant, magnification bias encodes important
cosmological information, and its inclusion leads to an alleviation of the
degeneracy between the galaxy bias and the amplitude normalisation of the
matter fluctuations.
