Litmus tests of the flat $\Lambda$CDM model and model-independent measurement of $H_0r_\mathrm{d}$ with LSST and DESI

In this analysis we apply a model-independent framework to test the flat $\Lambda$CDM cosmology using simulated SNIa data from the upcoming Legacy Survey of Space and Time (LSST) and combined with simulated Dark Energy Spectroscopic Instrument (DESI) five-years Baryon Acoustic Oscillations (BAO) data. We adopt an iterative smoothing technique to reconstruct the expansion history from SNIa data, which, when combined with BAO measurements, facilitates a comprehensive test of the Universe's curvature and the nature of dark energy. The analysis is conducted under four different mock true cosmologies: Two curvatures ($\Omega_{k,0}=0$ and 0.1) and two models of dark energy: a cosmological constant $\Lambda$ and the phenomenologically emergent dark energy. We forecast that our reconstruction technique can constrain cosmological parameters, such as the curvature ($\Omega_{k,0}$) and $c/(H_0 r_\mathrm{d})$, with spread due to the SNIa uncertainties up to $\pm 4\%$ and $\pm 0.1$ respectively, without assuming any form of dark energy.