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.

The assumptions of large-scale homogeneity and isotropy underly the familiar Friedmann-Lemaître-Robertson-Walker (FLRW) metric that appears to be an accurate description of our Universe. In this paper, we propose a new strategy of testing the validity of the FLRW metric, based on the galactic-scale lensing systems where strongly lensed gravitational waves and their electromagnetic counterparts can be simultaneously detected. Each strong lensing system creates opportunity to infer the curvature parameter of the Universe. Consequently, combined analysis of many such systems will provide a model-independent tool to test the validity of the FLRW metric. Our study demonstrates that the third-generation ground based GW detectors, like the Einstein Telescope (ET) and space-based detectors, like the Big Bang Observer (BBO), are promising concerning determination of the curvature parameter or possible detection of deviation from the FLRW metric. Such accurate measurements of the FLRW metric can become a milestone in precision GW cosmology.

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.

Gravitational wave experiments have entered a new stage which gets us closer to the opening a new observational window on the Universe. In particular, the Einstein Telescope (ET) is designed to have a fantastic sensitivity that will provide with tens or hundreds of thousand NS-NS inspiral events per year up to the redshift z = 2. Some of such events should be gravitationally lensed by intervening galaxies. We explore the prospects of observing gravitationally lensed inspiral NS-NS events in the Einstein telescope. Being conservative we consider the lens population of elliptical galaxies. It turns out that depending on the local insipral rate ET should detect from one per decade detection in the pessimistic case to a tens of detections per year for the most optimistic case. The detection of gravitationally lensed source in gravitational wave detectors would be an invaluable source of information concerning cosmography, complementary to standard ones (like supernovae or BAO) independent of the local cosmic distance ladder calibrations.