Which is a better cosmological probe: Number counts or cosmic magnification?

The next generation of cosmological surveys will have unprecedented measurement precision, hence they hold the power to put theoretical ideas to the most stringent tests yet. However, in order to realise the full potential of these measurements, we need to ensure that we apply the most effective analytical tools. We need to identify which cosmological observables are the best cosmological probes. Two commonly used cosmological observables are galaxy redshift number counts and cosmic magnification. Both of these observables have been investigated extensively in cosmological analyses, but only separately. In the light of interacting dark energy (IDE) emerging as a plausible means of alleviating current cosmological tensions, we investigate both observables on large scales in a universe with IDE, using the angular power spectrum: taking into account all known terms, including relativistic corrections, in the observed overdensity. Our results suggest that (given multi-tracer analysis) measuring relativistic effects with cosmic magnification will be relatively better than with galaxy redshift number counts, at all redshifts z. Conversely, without relativistic effects, galaxy redshift number counts will be relatively better in probing the imprint of IDE, at all z. At low z (up to around z = 0.1), relativistic effects enable cosmic magnification to be a relatively better probe of the IDE imprint; while at higher z (up to z < 3), galaxy redshift number counts become the better probe of IDE imprint. However, at z = 3 and higher, our results suggest that either of the observables will suffice.