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Register a new userTest of the cosmic distance duality relation for arbitrary spatial curvature
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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.
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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 $frac{{{D_L}}}{{{D_A}}}{(1 + z)^{ - 2}} =1+ eta z$.
We carry out a test of the cosmic distance duality relation using a sample of 52 SPT-SZ clusters, along with X-ray measurements from XMM-Newton. To carry out this test, we need an estimate of the luminosity distance ($D_L$) at the redshift of the cluster. For this purpose, we use three independent methods: directly using $D_L$ from the closest Type Ia Supernovae from the Union 2.1 sample, non-parametric reconstruction of $D_L$ using the same Union 2.1 sample, and finally using $H(z)$ measurements from cosmic chronometers and reconstructing $D_L$ using Gaussian Process regression. We use four different functions to characterize the deviations from CDDR. All our results for these ($4 times 3$) analyses are consistent with CDDR to within 1$sigma$.
In this paper, we propose a new test to the cosmic distance duality relation (CDDR), $D_L=D_A(1+z)^2$, where $D_L$ and $D_A$ are the luminosity and angular diameter distances, respectively. The data used correspond to 61 Type Ia Supernova luminosity distances and $Y_{SZE}-Y_X$ measurements of 61 galaxy clusters obtained by the {it Planck} mission and the deep XMM-Newton X-ray data, where $Y_{SZE}$ is the integrated comptonization parameter obtained via Sunyaev-Zeldovich effect observations and $Y_X$ is the X-ray counterpart. More precisely, we use the $Y_{SZE}D_{A}^{2}/C_{XSZE}Y_X$ scaling-relation and a deformed CDDR, such as $D_L/D_A(1+z)^2=eta(z)$, to verify if $eta(z)$ is compatible with the unity. Two $eta(z)$ functions are used, namely, $eta(z)=1+eta_0 z$ and $eta(z)=1+eta_0 z /(1+z)$. { We obtain that the CDDR validity ($eta_0=0$) is verified within $approx 1.5sigma$ c.l. for both $eta(z)$ functions.}.
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.
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.
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