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Future surveys of large-scale structure will be able to measure perturbationson the scale of the cosmological horizon, and so could potentially probe anumber of novel relativistic effects that are negligibly small on sub-horizonscales. These effects leave distinctive signatures in the power spectra ofclustering observables and, if measurable, would open a new window onrelativistic cosmology. We quantify the size and detectability of the effectsfor the most relevant future large-scale structure experiments: spectroscopicand photometric galaxy redshift surveys, intensity mapping surveys of neutralhydrogen, and radio continuum surveys. Our forecasts show that next-generationexperiments, reaching out to redshifts $z\simeq 4$, will not be able to detectpreviously-undetected general-relativistic effects by using individual tracersof the density field, although the contribution of weak lensing magnificationon large scales should be clearly detectable. We also perform a rigorous jointforecast for the detection of primordial non-Gaussianity through the excesspower it produces in the clustering of biased tracers on large scales, findingthat uncertainties of $\sigma(f_{\rm NL})\sim 1-2$ should be achievable. Westudy the level of degeneracy of these large-scale effects with severaltracer-dependent nuisance parameters, quantifying the minimal priors on thelatter that are needed for an optimal measurement of the former. Finally, wediscuss the systematic effects that must be mitigated to achieve this level ofsensitivity, and some alternative approaches that should help to improve theconstraints. The computational tools developed to carry out this study, whichrequires the full-sky computation of the theoretical angular power spectra for$\mathcal{O}(100)$ redshift bins, as well as realistic models of the luminosityfunction, are publicly available.

Ultra large-scale cosmology in next-generation experiments with single tracers