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Context.TheVera RubinObservatory will provide an unprecedented set of time-dependent observations of the sky. The planned Legacy Survey of Space and Time (LSST), operating for ten years, will provide dense light curves for thousands of active galactic nuclei (AGN) in deep drilling fields (DDFs) and less dense light curves for millions of AGN from the main survey (MS). Aims.We model the prospects for measuring the time delays for the AGN emission lines with respect to the continuum, using these data. Methods.We modeled the artificial light curves using the Timmer-König algorithm. We used the exemplary cadence to sample them (one for the MS and one for the DDF), we supplement light curves with the expected contamination by the strong emission lines (Hβ, Mg II, and CIV, as well as with Fe II pseudo-continuum and the starlight). We chose suitable photometric bands that are appropriate for the redshift and compared the assumed line time-delay with the recovered time delay for 100 statistical realizations of the light curves. Results.We show that time delays for emission lines can be well measured from the main survey for the bright tail of the quasar distribution (about 15% of all sources) with an accuracy within 1σerror. For the DDF, the results for fainter quasars are also reliable when the entire ten years of data are used. There are also some prospects to measure the time delays for the faintest quasars at the lowest redshifts from the first two years of data, and possibly even from the first season. The entire quasar population will allow us to obtain results of apparently high accuracy, but in our simulations, we see a systematic offset between the assumed and recovered time delay that depends on the redshift and source luminosity. This offset will not disappear even in the case of large statistics. This problem might affect the slope of the radius-luminosity relation and cosmological applications of quasars if no simulations are performed that correct for these effects. 

The standard model of cosmology has provided a good phenomenological description of a wide range of observations both at astrophysical and cosmological scales for several decades. This concordance model is constructed by a universal cosmological constant and supported by a matter sector described by the standard model of particle physics and a cold dark matter contribution, as well as very early-time inflationary physics, and underpinned by gravitation through general relativity. There have always been open questions about the soundness of the foundations of the standard model. However, recent years have shown that there may also be questions from the observational sector with the emergence of differences between certain cosmological probes. In this White Paper, we identify the key objectives that need to be addressed over the coming decade together with the core science projects that aim to meet these challenges. These discordances primarily rest on the divergence in the measurement of core cosmological parameters with varying levels of statistical confidence. These possible statistical tensions may be partially accounted for by systematics in various measurements or cosmological probes but there is also a growing indication of potential new physics beyond the standard model. After reviewing the principal probes used in the measurement of cosmological parameters, as well as potential systematics, we discuss the most promising array of potential new physics that may be observable in upcoming surveys. We also discuss the growing set of novel data analysis approaches that go beyond traditional methods to test physical models. These new methods will become increasingly important in the coming years as the volume of survey data continues to increase, and as the degeneracy between predictions of different physical models grows. There are several perspectives on the divergences between the values of cosmological parameters, such as the model-independent probes in the late Universe and model-dependent measurements in the early Universe, which we cover at length. The White Paper closes with a number of recommendations for the community to focus on for the upcoming decade of observational cosmology, statistical data analysis, and fundamental physics developments