We use 28 measurements of the Hubble parameter, H(z), at intermediate redshifts to determine the present-day Hubble constant H ₀ in four cosmological models. We measure , and Mpc⁻¹ (1σ errors) in the ΛCDM (spatially flat and non-flat), ωCDM, and ϕCDM models, respectively. These measured H ₀ values are more consistent with the lower values determined from recent data on the cosmic microwave background and baryon acoustic oscillations, as well as with the value found from a median statistical analysis of Huchra’s compilation of H ₀ measurements, but include the higher local measurements of H ₀ within the 2σ confidence limits.

We investigate two dark energy cosmological models (i.e., the ΛCDM and ϕCDM models) with massive neutrinos assuming two different neutrino mass hierarchies in both the spatially flat and non-flat scenarios, where in the ϕCDM model the scalar field possesses an inverse power-law potential, V(ϕ) ∝ ϕ ^−α (α > 0). Cosmic microwave background data from Planck 2015, baryon acoustic oscillation data from 6dFGS, SDSS-MGS, BOSS-LOWZ and BOSS CMASS-DR11, the joint light-curve analysis compilation of SNe Ia apparent magnitude observations, and the Hubble Space Telescope H ₀ prior, are jointly employed to constrain the model parameters. We first determine constraints assuming three species of degenerate massive neutrinos. In the spatially flat (non-flat) ΛCDM model, the sum of neutrino masses is bounded as Σm _ν < 0.165(0.299) eV at 95% confidence level (CL). Correspondingly, in the flat (non-flat) ϕCDM model, we find Σm _ν < 0.164(0.301) eV at 95% CL. The inclusion of spatial curvature as a free parameter results in a significant broadening of confidence regions for Σm _ν and other parameters. In the scenario where the total neutrino mass is dominated by the heaviest neutrino mass eigenstate, we obtain similar conclusions to those obtained in the degenerate neutrino mass scenario. In addition, the results show that the bounds on Σm _ν based on two different neutrino mass hierarchies have insignificant differences in the spatially flat case for both the ΛCDM and ϕCDM models; however, the corresponding differences are larger in the non-flat case.

We systematically explore the influence of the prior of the peak absolute magnitude (M) of Type Ia supernovae (SNe Ia) on the measurement of the Hubble constant (H ₀) from SNe Ia observations. We consider five different data-motivated M priors, representing varying levels of dispersion, and assume the spatially flat ΛCDM cosmological model. Different M priors lead to relative changes in the mean values of H ₀ from 2% to 7%. Loose priors on M yield H ₀ estimates consistent with both the Planck 2018 result and the SH0ES result at the 68% confidence level. We also examine the potential impact of peculiar velocity subtraction on the value of H ₀ and show that it is insignificant for the SNe Ia observations with redshift z > 0.01 used in our analyses. We also repeat the analysis in the cosmography model and find very similar results. This suggests that our results are robust and model independent.

Galaxy–galaxy strong gravitational lensing (GGSL) is a powerful probe for the formation and evolution of galaxies and cosmology, while the sample size of GGSLs leads to considerable uncertainties and potential bias. The China Space Station Telescope (CSST, to be launched in late 2026) will conduct observations across 17 500 square degrees of the sky, capturing images in the |$ugriz$| bands with a spatial resolution comparable to that of the Hubble Space Telescope. We ran a set of Monte Carlo simulations to predict that the CSST’s wide-field survey will observe |$\sim$|160 000 galaxy–galaxy strong lenses over its lifespan, increasing the number of existing galaxy–galaxy strong lens samples by three orders of magnitude. This is comparable to the capabilities of the |$\it Euclid$| telescope but with the added benefit of additional colour information. Specifically, the CSST can detect strong lenses with Einstein radii about |$0.64\pm 0.42 ^{\prime \prime }$|⁠, corresponding to the velocity dispersions of |$217.19 \pm 50.55 \, \text{km/s}$|⁠. These lenses exhibit a median magnification of |$\sim$|5. The apparent magnitude of the unlensed sources in the g band is |$25.87 \pm 1.19$|⁠. The signal-to-noise ratio of the lensed images covers a range of |${\sim} 20$| to |${\sim} 1000$|⁠, allowing us to determine the Einstein radius with an accuracy ranging from |${\sim} 1~{{\ \rm per\ cent}}$| to |${\sim} 0.1~{{\ \rm per\ cent}}$|⁠, ignoring various modelling systematics. Our estimates indicate that CSST can observe rare systems like double source-plane and spiral galaxy lenses. The above selection functions of the CSST strong lensing observation help optimize the strategy of finding and modelling GGSLs.

Einstein’s theory of general relativity (GR) has been precisely tested on solar system scales, but extragalactic tests are still poorly performed. In this work, we use a newly compiled sample of galaxy-scale strong gravitational lenses to test the validity of GR on kiloparsec scales. In order to solve the circularity problem caused by the presumption of a specific cosmological model based on GR, we employ the distance sum rule in the Friedmann–Lemaître–Robertson–Walker metric to directly estimate the parameterized post-Newtonian (PPN) parameter γ _PPN and the cosmic curvature Ω _k by combining observations of strong lensing and Type Ia supernovae. This is the first simultaneous measurement of γ _PPN and Ω _k without any assumptions about the contents of the universe or the theory of gravity. Our results show that γ PPN = 1.11 − 0.09 + 0.11 and Ω k = 0.48 − 0.71 + 1.09 , indicating a strong degeneracy between the two quantities. The measured γ _PPN, which is consistent with the prediction of 1 from GR, provides a precise extragalactic test of GR with a fractional accuracy better than 9.0%. If a prior of the spatial flatness (i.e., Ω _k = 0) is adopted, the PPN parameter constraint can be further improved to γ PPN = 1.07 − 0.07 + 0.07 , representing a precision of 6.5%. On the other hand, in the framework of GR (i.e., γ _PPN = 1), our results are still marginally compatible with zero curvature ( Ω k = − 0.12 − 0.36 + 0.48 ), supporting no significant deviation from a flat universe.