  Upcoming galaxy surveys will allow us to probe the growth of the cosmic
large-scale structure with improved sensitivity compared to current missions,
and will also map larger areas of the sky. This means that in addition to the
increased precision in observations, future surveys will also access the
ultra-large-scale regime, where commonly neglected effects such as lensing,
redshift-space distortions and relativistic corrections become important for
calculating correlation functions of galaxy positions. At the same time,
several approximations usually made in these calculations, such as the Limber
approximation, break down at those scales. The need to abandon these
approximations and simplifying assumptions at large scales creates severe
issues for parameter estimation methods. On the one hand, exact calculations of
theoretical angular power spectra become computationally expensive, and the
need to perform them thousands of times to reconstruct posterior probability
distributions for cosmological parameters makes the approach unfeasible. On the
other hand, neglecting relativistic effects and relying on approximations may
significantly bias the estimates of cosmological parameters. In this work, we
quantify this bias and investigate how an incomplete modelling of various
effects on ultra-large scales could lead to false detections of new physics
beyond the standard $\Lambda$CDM model. Furthermore, we propose a simple
debiasing method that allows us to recover true cosmologies without running the
full parameter estimation pipeline with exact theoretical calculations. This
method can therefore provide a fast way of obtaining accurate values of
cosmological parameters and estimates of exact posterior probability
distributions from ultra-large-scale observations.
