No Arabic abstract
General relativity reproduces main current cosmological observations, assuming the validity of 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 (SN Ia) and that of the Cosmic Microwave background (CMB). 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 $zsim 3$. Such accurate model-independent test of fundamental cosmological principles can become a milestone in precision cosmology.
Recently, two classes of quasar samples were identified, which are promising as new cosmological probes extending to higher redshifts. The first sample uses the nonlinear relation between the ultraviolet and X-ray luminosities of quasars to derive luminosity distances, whereas the linear sizes of compact radio quasars in the second sample can serve as standardized rulers, providing angular-diameter distances. In this study, under the assumption of a flat universe, we refreshed the calibration of multiple measurements of high-redshift quasars (in the framework of a cosmological-model-independent method with the newest Hubble parameters data). Furthermore, we placed constraints on four models that characterize the cosmic equation of state ($w$). The obtained results show that: 1) the two quasar samples could provide promising complementary probes at much higher redshifts, whereas compact radio quasars perform better than ultraviolet and X-ray quasars at the current observational level; 2) strong degeneracy between the cosmic equation of state ($w$) and Hubble constant ($H_0$) is revealed, which highlights the importance of independent determination of $H_0$ from time-delay measurements of strongly lensed Quasars; 3)together with other standard ruler probes, such as baryon acoustic oscillation distance measurements, the combined QSO+BAO measurements are consistent with the standard $Lambda$CDM model at a constant equation of state $w=-1$; 4) ranking the cosmological models, the polynomial parametrization gives a rather good fit among the four cosmic-equation-of-state models, whereas the Jassal-Bagla-Padmanabhan (JBP) parametrization is substantially penalized by the Akaike Information Criterion and Bayesian Information Criterion criterion.
In metric theories of gravity with photon number conservation, the luminosity and angular diameter distances are related via the Etherington relation, also known as the distance-duality relation (DDR). A violation of this relation would rule out the standard cosmological paradigm and point at the presence of new physics. We quantify the ability of Euclid, in combination with contemporary surveys, to improve the current constraints on deviations from the DDR in the redshift range $0<z<1.6$. We start by an analysis of the latest available data, improving previously reported constraints by a factor of 2.5. We then present a detailed analysis of simulated Euclid and external data products, using both standard parametric methods (relying on phenomenological descriptions of possible DDR violations) and a machine learning reconstruction using Genetic Algorithms. We find that for parametric methods Euclid can (in combination with external probes) improve current constraints by approximately a factor of six, while for non-parametric methods Euclid can improve current constraints by a factor of three. Our results highlight the importance of surveys like Euclid in accurately testing the pillars of the current cosmological paradigm and constraining physics beyond the standard cosmological model.
The construction of the cosmic distance-duality relation (CDDR) has been widely studied. However, its consistency with various new observables remains a topic of interest. We present a new way to constrain the CDDR $eta(z)$ using different dynamic and geometric properties of strong gravitational lenses (SGL) along with SNe Ia observations. We use a sample of $102$ SGL with the measurement of corresponding velocity dispersion $sigma_0$ and Einstein radius $theta_E$. In addition, we also use a dataset of $12$ two image lensing systems containing the measure of time delay $Delta t$ between source images. Jointly these two datasets give us the angular diameter distance $D_{A_{ol}}$ of the lens. Further, for luminosity distance, we use the $740$ observations from JLA compilation of SNe Ia. To study the combined behavior of these datasets we use a model independent method, Gaussian Process (GP). We also check the efficiency of GP by applying it on simulated datasets, which are generated in a phenomenological way by using realistic cosmological error bars. Finally, we conclude that the combined bounds from the SGL and SNe Ia observation do not favor any deviation of CDDR and are in concordance with the standard value ($eta=1$) within $2sigma$ confidence region, which further strengthens the theoretical acceptance of CDDR.
The cosmic distance duality relation (CDDR), eta(z)=(1+z)^2 d_A(z)/d_L(z)=1, is one of the most fundamental and crucial formulae in cosmology. This relation couples the luminosity and angular diameter distances, two of the most often used measures of structure in the Universe. We here propose a new model-independent method to test this relation, using strong gravitational lensing (SGL) and the high-redshift quasar Hubble diagram reconstructed with a Bezier parametric fit. We carry out this test without pre-assuming a zero spatial curvature, adopting instead the value Omega_K=0.001 +/- 0.002 optimized by Planck in order to improve the reliability of our result. We parametrize the CDDR using eta(z)=1 + eta_0 z, 1 + eta_1 z + eta_2 z^2 and 1 + eta_3 z/(1+z), and consider both the SIS and non-SIS lens models for the strong lensing. Our best fit results are: eta_0=-0.021^{+0.068}_{-0.048}, eta_1=-0.404^{+0.123}_{-0.090}, eta_2=0.106^{+0.028}_{-0.034}, and eta_3=-0.507^{+0.193}_{-0.133} for the SIS model, and eta_0=-0.109^{+0.044}_{-0.031} for the non-SIS model. The measured eta(z), based on the Planck parameter Omega_K, is essentially consistent with the value (=1) expected if the CDDR were fully respected. For the sake of comparison, we also carry out the test for other values of Omega_K, but find that deviations of spatial flatness beyond the Planck optimization are in even greater tension with the CDDR. Future measurements of SGL may improve the statistics and alter this result but, as of now, we conclude that the CDDR favours a flat Universe.
A distance-deviation consistency and model-independent method to test the cosmic distance duality relation (CDDR) is provided. The method is worth attention on two aspects: firstly, a distance-deviation consistency method is used to pair subsamples: instead of pairing subsamples with redshift deviation smaller than a textbf{value}, say $leftvert Delta zrightvert <0.005$. The redshift deviation between subsamples decreases with the redshift to ensure the distance deviation stays the same. The method selects more subsamples at high redshift, up to $z=2.16$, and provides 120 subsample pairs. Secondly, the model-independent method involves the latest data set of $1048$ type Ia supernovae (SNe Ia) and $205$ strong gravitational lensing systems (SGLS), which are used to obtain the luminosity distances $D_L$ and the ratio of angular diameter distance $D_A$ respectively. With the model-independent method, parameters of the CDDR, the SNe Ia light-curve, and the SGLS are fitted simultaneously. textbf{The result shows} that $eta = 0.047^{+0.190}_{-0.151}$ and CDDR is validated at 1$sigma$ confidence level for the form $frac{{{D_L}}}{{{D_A}}}{(1 + z)^{ - 2}} =1+ eta z$.