Under very general assumptions of the metric theory of spacetime, photons traveling along null geodesics and photon number conservation, two observable concepts of cosmic distance, i.e., the angular diameter and the luminosity distances are related to each other by the so-called distance duality relation (DDR) . Observational validation of this relation is quite important because any evidence of its violation could be a signal of new physics. In this paper we introduce a new method to test the DDR based on strong gravitational lensing systems and type Ia supernovae (SNe Ia) under a flat universe. The method itself is worth attention because unlike previously proposed techniques, it does not depend on all other prior assumptions concerning the details of cosmological model. We tested it using a new compilation of strong lensing (SL) systems and JLA compilation of SNe Ia and found no evidence of DDR violation. For completeness, we also combined it with previous cluster data and showed its power on constraining the DDR. It could become a promising new probe in the future in light of forthcoming massive SL surveys and because of expected advances in galaxy cluster modeling.

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.

The two-point diagnostics Om(z _i , z _j ) and Omh ²(z _i , z _j ) have been introduced as an interesting tool for testing the validity of the Λ cold dark matter (ΛCDM) model. Recently, Sahni et al. combined two independent measurements of H(z) from baryon acoustic oscillation (BAO) data with the value of the Hubble constant H ₀, and used the second of these diagnostics to test the ΛCDM (a constant equation-of-state parameter for dark energy) model. Their result indicated a considerable tension between observations and predictions of the ΛCDM model. Since reliable data concerning the expansion rates of the universe at different redshifts H(z) are crucial for the successful application of this method, we investigate both two-point diagnostics on the most comprehensive set of N = 36 measurements of H(z) from BAOs and the differential ages (DAs) of passively evolving galaxies. We discuss the uncertainties of the two-point diagnostics and find that they are strongly non-Gaussian and follow the patterns deeply rooted in their very construction. Therefore we propose that non-parametric median statistics is the most appropriate way of treating this problem. Our results support the claims that ΛCDM is in tension with H(z) data according to the two-point diagnostics developed by Shafieloo, Sahni, and Starobinsky. However, other alternatives to the ΛCDM model, such as the wCDM or Chevalier–Polarski–Linder models, perform even worse. We also note that there are serious systematic differences between the BAO and DA methods that ought to be better understood before H(z) measurements can compete with other probes methods.

General relativity reproduces main current cosmological observations, assuming the validity of the cosmic distance duality relation (CDDR) at all scales and epochs. However, CDDR is poorly tested in the redshift interval between the farthest observed Type Ia supernovae and that of the cosmic microwave background. We present a new idea of testing the validity of CDDR, through the multiple measurements of high-redshift quasars. Luminosity distances are derived from the relation between the UV and X-ray luminosities of quasars, while angular diameter distances are obtained from the compact structure in radio quasars. This will create a valuable opportunity where two different cosmological distances from the same kind of objects at high redshifts are compared. Our constraints are more stringent than other currently available results based on different observational data and show no evidence for the deviation from CDDR at z ∼ 3. Such an accurate model-independent test of fundamental cosmological principles can become a milestone in precision cosmology.