In this paper, based on a 2.29 GHz VLBI all-sky survey of 613 milliarcsecond ultra-compact radio sources with 0.0035<z<3.787, we describe a method of identifying the sub-sample which can serve as individual standard rulers in cosmology. If the linear size of the compact structure is assumed to depend on source luminosity and redshift as l_m=l L^β (1+z)ⁿ, only intermediate-luminosity quasars (10²⁷ W/Hz<L< 10²⁸ W/Hz) show negligible dependence (|n| 10⁻³, |β| 10⁻⁴), and thus represent a population of such rulers with fixed characteristic length l=11.42 pc. With a sample of 120 such sources covering the redshift range 00.46<z<2.8, we confirm the existence of dark energy in the Universe with high significance under the assumption of a flat universe, and obtain stringent constraints on both the matter density Ω_m=0.323^+0.245_−0.145 and the Hubble constant H₀=66.30^+7.00_−8.50 km sec⁻¹ Mpc⁻¹. Finally, with the angular diameter distances D_A measured for quasars extending to high redshifts (0z~ 3.), we reconstruct the D_A(z) function using the technique of Gaussian processes. This allows us to identify the redshift corresponding to the maximum of the D_A(z) function: 0z_m=1.7 and the corresponding angular diameter distance D_A(z_m)=1719.01±43.46 Mpc. Similar reconstruction of the expansion rate function H(z) based on the data from cosmic chronometers and BAO gives us H(z_m)=176.77±6.11 km sec⁻¹ Mpc⁻¹. These measurements are used to estimate the speed of light: c=3.039(±0.180)× 10⁵ km/s. This is the first measurement of the speed of light in a cosmological setting referring to the distant past.

Using a new recently compiled milliarcsecond compact radio data set of 120 intermediate-luminosity quasars in the redshift range \(0.46< z <2.76\), whose statistical linear sizes show negligible dependence on redshifts and intrinsic luminosity and thus represent standard rulers in cosmology, we constrain three viable and most popular f(T) gravity models, where T is the torsion scalar in teleparallel gravity. Our analysis reveals that constraining power of the quasars data (\(N=120\)) is comparable to the Union2.1 SN Ia data (\(N=580\)) for all three f(T) models. Together with other standard ruler probes such as cosmic microwave background and baryon acoustic oscillation distance measurements, the present value of the matter density parameter \(\Omega _\mathrm{m}\) obtained by quasars is much larger than that derived from other observations. For one of the models considered (\(f_1\)CDM) a small but noticeable deviation from \(\Lambda \)CDM cosmology is present, while in the framework of \(f_3\)CDM the effective equation of state may cross the phantom divide line at lower redshifts. These results indicate that intermediate-luminosity quasars could provide an effective observational probe comparable to SN Ia at much higher redshifts, and f(T) gravity is a reasonable candidate for the modified gravity theory.

Although the Hubble constant H₀ and spatial curvature Ω_K have been measured with very high precision, they still suffer from some tensions. In this paper, we propose an improved method to combine the observations of ultracompact structure in radio quasars and strong gravitational lensing with quasars acting as background sources to determine H₀ and Ω_K simultaneously. By applying the distance sum rule to the time-delay measurements of seven strong lensing systems and 120 intermediate-luminosity quasars calibrated as standard rulers, we obtain stringent constraints on the Hubble constant (H₀ = 78.3 ± 2.9 km s⁻¹ Mpc⁻¹) and the cosmic curvature (Ω_K = 0.49 ± 0.24). On the one hand, in the framework of a flat universe, the measured Hubble constant (⁠|$H_0=73.6^{+1.8}_{-1.6} \mathrm{\,km\,s^{-1}\,Mpc^{-1}}$|⁠) is strongly consistent with that derived from the local distance ladder, with a precision of 2 per cent. On the other hand, if we use the local H₀ measurement as a prior, our results are marginally compatible with zero spatial curvature (⁠|$\Omega _K=0.23^{+0.15}_{-0.17}$|⁠) and there is no significant deviation from a flat universe. Finally, we also evaluate whether strongly lensed quasars would produce robust constraints on H₀ and Ω_K in the non-flat and flat Λ cold dark matter model, if the compact radio structure measurements are available from very long baseline interferometry observations.

In this paper, we quantify the ability of multiple measurements of high-redshift quasars to constrain several theories of modified gravity, including the Dvali–Gabadadze–Porrati braneworld scenario, generalized Chaplygin gas, f(T) modified gravity, and modified polytropic Cardassian model. Recently released sample of 1598 quasars with X-ray and ultraviolet flux measurements in the redshift range of 0.036 ≤ z ≤ 5.1003, as well as a compilation of 120 intermediate-luminosity radio quasars covering the redshift of 0.46 < z < 2.76 are respectively used as standard probes at higher redshifts. For all considered modified gravity theories, our results show that there is still some possibility that the standard Λ cold dark matter (ΛCDM) scenario might not be the best cosmological model preferred by the current quasar observations. In order to improve cosmological constraints, the quasar data are also combined with the latest observations of baryon acoustic oscillations, which strongly complement the constraints. Finally, we discuss the support given by the data to modified gravity theories, applying different information theoretic techniques like the Akaike information criterion, Bayesian information criterion, and Jensen–Shannon divergence.

Astrophysical observations provide a unique opportunity to test possible signatures of Lorentz invariance violation (LIV), due to the high energies and long distances involved. In quantum theory of gravity, one may expect the modification of the dispersion relation between energy and momentum for photons, which can be probed with the time lag (the arrival time delay between light curves in different energy bands) of gamma-ray bursts (GRBs). In this paper, by using the detailed time delay measurements of GRB 160625B at different energy bands, as well as 23 time delay GRBs covering the redshift range of z = 0.168–2.5 (which were measured at different energy channels from the light curves), we propose an improved model-independent method (based on the newly compiled sample of H(z) measurements) to probe the energy-dependent velocity due to the modified dispersion relation for photons. In the framework of a more complex and reasonable theoretical expression to describe the time delays, our results imply that the intrinsic time lags can be better described with more GRB time delay data. More importantly, through direct fitting of the time delay measurements of a sample of GRBs, our limit on the LIV energy scale is comparable to that with unknown constant for the intrinsic time lag, much lower than the Planck energy scale in both linear LIV and quadratic LIV cases.

The cosmic curvature, a fundamental parameter for cosmology could hold deep clues to inflation and cosmic origins. We propose an improved model-independent method to constrain the cosmic curvature by combining the constructed Hubble diagram of high-redshift quasars with galactic-scale strong lensing systems expected to be seen by the forthcoming LSST survey. More specifically, the most recent quasar data are used as a new type of standard candles in the range 0.036 < z < 5.100, whose luminosity distances can be directly derived from the non-linear relation between X-ray and UV luminosities. Compared with other methods, the proposed one involving the quasar data achieves constraints with higher precision (ΔΩ_k ∼ 10⁻²) at high redshifts (z ∼ 5.0). We also investigate the influence of lens mass distribution in the framework of three types of lens models extensively used in strong lensing studies (SIS model, power-law spherical model, and extended power-law lens model), finding the strong correlation between the cosmic curvature and the lens model parameters. When the power-law mass density profile is assumed, the most stringent constraint on the cosmic curvature Ω_k can be obtained. Therefore, the issue of mass density profile in the early-type galaxies is still a critical one that needs to be investigated further.