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Time-delay cosmography is a powerful technique to constrain cosmological parameters, particularly the Hubble constant (H₀). The TDCOSMO Collaboration is performing an ongoing analysis of lensed quasars to constrain cosmology using this method. In this work, we obtain constraints from the lensed quasar WGD 2038−4008 using new time-delay measurements and previous mass models by TDCOSMO. This is the first TDCOSMO lens to incorporate multiple lens modeling codes and the full time-delay covariance matrix into the cosmological inference. The models are fixed before the time delay is measured, and the analysis is performed blinded with respect to the cosmological parameters to prevent unconscious experimenter bias. We obtainD_Δt = 1.68_−0.38^+0.40Gpc using two families of mass models, a power-law describing the total mass distribution, and a composite model of baryons and dark matter, although the composite model is disfavored due to kinematics constraints. In a flat ΛCDM cosmology, we constrain the Hubble constant to beH₀ = 65₋₁₄⁺²³km s⁻¹Mpc⁻¹. The dominant source of uncertainty comes from the time delays, due to the low variability of the quasar. Future long-term monitoring, especially in the era of theVera C. RubinObservatory’s Legacy Survey of Space and Time, could catch stronger quasar variability and further reduce the uncertainties. This system will be incorporated into an upcoming hierarchical analysis of the entire TDCOSMO sample, and improved time delays and spatially-resolved stellar kinematics could strengthen the constraints from this system in the future. 

Context. Persistent tension between low-redshift observations and the cosmic microwave background radiation (CMB), in terms of two fundamental distance scales set by the sound horizon r d and the Hubble constant H 0 , suggests new physics beyond the Standard Model, departures from concordance cosmology, or residual systematics. Aims. The role of different probe combinations must be assessed, as well as of different physical models that can alter the expansion history of the Universe and the inferred cosmological parameters. Methods. We examined recently updated distance calibrations from Cepheids, gravitational lensing time-delay observations, and the tip of the red giant branch. Calibrating the baryon acoustic oscillations and type Ia supernovae with combinations of the distance indicators, we obtained a joint and self-consistent measurement of H 0 and r d at low redshift, independent of cosmological models and CMB inference. In an attempt to alleviate the tension between late-time and CMB-based measurements, we considered four extensions of the standard ΛCDM model. Results. The sound horizon from our different measurements is r d  = (137 ± 3 stat.  ± 2 syst. ) Mpc based on absolute distance calibration from gravitational lensing and the cosmic distance ladder. Depending on the adopted distance indicators, the combined tension in H 0 and r d ranges between 2.3 and 5.1 σ , and it is independent of changes to the low-redshift expansion history. We find that modifications of ΛCDM that change the physics after recombination fail to provide a solution to the problem, for the reason that they only resolve the tension in H 0 , while the tension in r d remains unchanged. Pre-recombination extensions (with early dark energy or the effective number of neutrinos N eff  = 3.24 ± 0.16) are allowed by the data, unless the calibration from Cepheids is included. Conclusions. Results from time-delay lenses are consistent with those from distance-ladder calibrations and point to a discrepancy between absolute distance scales measured from the CMB (assuming the standard cosmological model) and late-time observations. New proposals to resolve this tension should be examined with respect to reconciling not only the Hubble constant but also the sound horizon derived from the CMB and other cosmological probes. 

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