In this letter we propose a new and model-independent cosmological test for the distance-duality (DD) relation, η = D L (z)(1 + z) −2 /D A (z) = 1, where D L and D A are, respectively, the luminosity and angular diameter distances. For D L we consider two sub-samples of SNe type Ia taken from Constitution data (2009) whereas D A distances are provided by two samples of galaxy clusters compiled by De Fillipis et al. (2005) and Bonamente et al. (2006) by combining Sunyaev-Zeldovich effect (SZE) and X-ray surface brightness. The SNe Ia redshifts of each sub-sample were carefully chosen to coincide with the ones of the associated galaxy cluster sample (∆z < 0.005) thereby allowing a direct test of DD relation. Since for very low redshifts, D A (z) ≅ D L (z), we have tested the DD relation by assuming that η is a function of the redshift parametrized by two different expressions: η(z) = 1 + η 0 z and η(z) = 1 + η 0 z/(1 + z), where η 0 is a constant parameter quantifying a possible departure from the strict validity of the reciprocity relation (η 0 = 0). In the best scenario (linear parametrization) we obtain η 0 = −0.28 +0.44 −0.44 (2σ, statistical + systematic errors) for de Fillipis et al. sample (elliptical geometry), a result only marginally compatible with the DD relation. However, for Bonamente et al. sample (spherical geometry) the constraint is η 0 = −0.42 +0.34 −0.34 (3σ, statistical + systematic errors) which is clearly incompatible with the duality-distance relation.

Context. Observations in the cosmological domain are heavily dependent on the validity of the cosmic distance-duality (DD) relation, η = D L (z)(1 + z) 2 /D A (z) = 1, an exact result required by the Etherington reciprocity theorem where D L (z) and D A (z) are, respectively, the luminosity and angular diameter distances. In the limit of very small redshifts D A (z) = D L (z) and this ratio is trivially satisfied. Measurements of Sunyaev-Zeldovich effect (SZE) and X-rays combined with the DD relation have been used to determine D A (z) from galaxy clusters. This combination offers the possibility of testing the validity of the DD relation, as well as determining which physical processes occur in galaxy clusters via their shapes. Aims. We use WMAP (7 years) results by fixing the conventional ΛCDM model to verify the consistence between the validity of DD relation and different assumptions about galaxy cluster geometries usually adopted in the literature. Methods. We assume that η is a function of the redshift parametrized by two different relations: η(z) = 1+η 0 z, and η(z) = 1+η 0 z/(1+z), where η 0 is a constant parameter quantifying the possible departure from the strict validity of the DD relation. In order to determine the probability density function (PDF) of η 0 , we consider the angular diameter distances from galaxy clusters recently studied by two different groups by assuming elliptical (isothermal) and spherical (non-isothermal) β models. The strict validity of the DD relation will occur only if the maximum value of η 0 PDF is centered on η 0 = 0. Results. It was found that the elliptical β model is in good agreement with the data, showing no violation of the DD relation (PDF peaked close to η 0 = 0 at 1σ), while the spherical (non-isothermal) one is only marginally compatible at 3σ. Conclusions. The present results derived by combining the SZE and X-ray surface brightness data from galaxy clusters with the latest WMAP results (7-years) favors the elliptical geometry for galaxy clusters. It is remarkable that a local property like the geometry of galaxy clusters might be constrained by a global argument provided by the cosmic DD relation.

Testing the cosmic distance duality relation (CDDR) constitutes an important task for cosmology and fundamental physics since any violation of it would be a clear evidence of new physics. In this paper, we propose a new test for the CDDR using only current measurements of the gas mass fraction of galaxy clusters from Sunyaev-Zeldovich (fSZE) and X-ray surface brightness (fX−ray) observations. We show that the relation between fX−ray and fSZE observations is given by fSZE = ηfX−ray, where η quantifies deviations from the CDDR. Since this latter expression is valid for the same object in a given galaxy cluster sample, the method proposed removes possible contaminations from different systematics error sources and redshift differences involved in luminosity and angular diameter distance measurements. We apply this cosmological model-independent methodology to the most recent fX−ray and fSZE data and show that no significant violation of the CDDR is found. 98.80.Es, 98.65.Cw

We use current measurements of the expansion rate H(z) and cosmic background radiation bounds on the spatial curvature of the Universe to impose cosmological model-independent constraints on cosmic opacity. To perform our analyses, we compare opacity-free distance modulus from H(z) data with those from two type Ia supernovae compilations, namely, the Union2.1 plus the most distant spectroscopically confirmed SNe Ia (SCP-0401 at z = 1.713) and two Sloan Digital Sky Survey (SDSS) subsamples. We find that a completely transparent universe is in full agreement with the Union 2.1 + SNe Ia SCP-0401 sample. For the SDSS compilations, such universe is compatible with observations at < 1.5σ level regardless the SNe Ia light-curve fitting used.

The cosmic distance duality relation is a milestone of cosmology involving the luminosity and angular diameter distances. Any departure of the relation points to new physics or systematic errors in the observations, therefore tests of the relation are extremely important to build a consistent cosmological framework. Here, two new tests are proposed based on galaxy clusters observations (angular diameter distance and gas mass fraction) and H(z) measurements. By applying Gaussian Processes, a non-parametric method, we are able to derive constraints on departures of the relation where no evidence of deviation is found in both methods, reinforcing the cosmological and astrophysical hypotheses adopted so far.

We propose and perform a new test of the cosmic distance-duality relation (CDDR), DL(z)/DA(z)(1 + z) 2 = 1, where DA is the angular diameter distance and DL is the luminosity distance to a given source at redshift z, using strong gravitational lensing (SGL) and type Ia Supernovae (SNe Ia) data. We show that the ratio D = DA 12 /DA 2 and D * = DL 12 /DL 2 , where the subscripts 1 and 2 correspond, respectively, to redshifts z1 and z2, are linked by D/D * = (1 + z1) 2 if the CDDR is valid. We allow departures from the CDDR by defining two functions for η(z1), which equals unity when the CDDR is valid. We find that combination of SGL and SNe Ia data favours no violation of the CDDR at 1σ confidence level (η(z) ≃ 1), in complete agreement with other tests and reinforcing the theoretical pillars of the CDDR.

Measurements of strong gravitational lensing jointly with type Ia supernovae (SNe Ia) observations have been used to test the validity of the cosmic distance duality relation (CDDR), DL(z)/[(1 + z) 2 DA(z)] = η = 1, where DL(z) and DA(z) are the luminosity and the angular diameter distances to a given redshift z, respectively. However, several lensing systems lie in the interval 1.4 ≤ z ≤ 3.6 i.e., beyond the redshift range of current SNe Ia compilations (z ≈ 1.50), which prevents this kind of test to be fully explored. In this paper, we circumvent this problem by testing the CDDR considering observations of strong gravitational lensing along with SNe Ia and a subsample from the latest gamma-ray burst distance modulus data, whose redshift range is 0.033 ≤ z ≤ 9.3. We parameterize their luminosity distances with a second degree polynomial function and search for possible deviations from the CDDR validity by using four different η(z) functions: η(z) = 1 + η0z, η(z) = 1 + η0z/(1 + z), η(z) = (1 + z) η 0 and η(z) = 1 + η0 ln(1 + z). Unlike previous tests done at redshifts lower than 1.50, the likelihood for η0 depends strongly on the η(z) function considered, but we find no significant deviation from the CDDR validity (η0 = 0). However, our analyses also point to the fact that caution is needed when one fits data in higher redshifts to test the CDDR as well as a better understanding of the mass distribution of lenses also is required for more accurate results.

In this Letter, we discuss a new cosmological‐model‐independent test for the cosmic distance duality relation (CDDR), η=DL(L)(1 +z)−2/DA(z) = 1, where DA(z) and DL(z) are the angular diameter and luminosity distances, respectively. Using the general expression for X‐ray gas mass fraction (fgas) of galaxy clusters, fgas∝DLDA1/2, we show that fgas observations jointly with Type Ia supernovae (SNe Ia) data furnish a validity test for the CDDR. To perform our analysis, we use 38 fgas measurements recently studied by two groups considering different assumptions to describe the clusters and two subsamples of SNe Ia distance luminosity extracted from the Union2 compilation. In our test, we consider the η parameter as a function of the redshift parametrized by two different functional forms. It is found that the La Roque et al. sample is in perfect agreement with the duality relation (η= 1), whereas the Ettori et al. sample presents a significant conflict.