Abstract: We perform a cosmological-model-independent test for the distance-duality (DD) relation $\eta(z)=D_L(z)(1+z)^{-2}/D_A(z)$, where $D_L$ and $D_A$ are the luminosity distance and angular diameter distance respectively, with a combination of observational data for $D_L$ taken from the latest Union2 SNe Ia and that for $D_A$ provided by two galaxy clusters samples compiled by De Filippis {\it et al.} and Bonamente {\it et al.}. Two parameterizations for $\eta(z)$, i.e., $\eta(z)=1+\eta_0z$ and $\eta(z)=1+\eta_0z/(1+z)$, are used. We find that the DD relation can be accommodated at $1\sigma$ confidence level (CL) for the De Filippis {\it et al.} sample and at $3\sigma$ CL for the Bonamente {\it et al.} sample. We also examine the DD relation by postulating two more general parameterizations: $\eta(z)=\eta_0+\eta_1z$ and $\eta(z)=\eta_0+\eta_1z/(1+z)$, and find that the DD relation is compatible with the results from the De Filippis {\it et al.} and the Bonamente {\it et al.} samples at $1\sigma$ and $2\sigma$ CLs, respectively. Thus, we conclude that the DD relation is compatible with present observations.

Abstract: We study the validity of cosmic distance duality relation between angular diameter and luminosity distances. To test this duality relation we use the latest Union2 Supernovae Type Ia (SNe Ia) data for estimating the luminosity distance. The estimation of angular diameter distance comes from the samples of galaxy clusters (real and mock) and FRIIb radio galaxies. We parameterize the distance duality relation as a function of redshift in six different ways. Our results rule out some of the parameterizations significantly.

Abstract: We study the validity of cosmic distance duality relation between angular diameter and luminosity distances. To test this duality relation we use the latest Union2 Supernovae Type Ia (SNe Ia) data for estimating the luminosity distance. The estimation of angular diameter distance comes from the samples of galaxy clusters (real and mock) and FRIIb radio galaxies. We parameterize the distance duality relation as a function of redshift in six different ways. Our results rule out some of the parameterizations significantly.

Abstract: Baryon acoustic oscillations imprinted in the galaxy power spectrum can be used as a standard ruler to determine the angular diameter distance and Hubble parameter from high-redshift galaxies. Combining redshift distortion effect which apparently distorts the galaxy clustering pattern, we can also constrain the growth rate of large-scale structure formation. Usually, future forecasts for constraining these parameters from galaxy redshift surveys are made with the full 2D power spectrum characterized as a function of wave number $k$ and directional cosine $\ensuremath{\mu}$ between line-of-sight direction and wave vector, i.e., $P(k,\ensuremath{\mu})$. Here, we apply the multipole expansion to the full 2D power spectrum, and discuss how much cosmological information can be extracted from the lower-multipole spectra, taking a proper account of the nonlinear effects on gravitational clustering and redshift distortion. Fisher matrix analysis reveals that compared to the analysis with the full 2D spectrum, using only the partial information from the monopole and quadrupole spectra generally degrades the constraints by a factor of $\ensuremath{\sim}1.3$ for each parameter. The additional information from the hexadecapole spectrum helps to improve the constraints, leading to a result that is almost comparable to the one expected from the full 2D spectrum.

Abstract: The standard analysis of the CMB data assumes that the distance to the last scattering surface can be calculated using the distance-redshift relation as in the Friedmann model. However, in the inhomogeneous universe, even if =0, the distance relation is not the same as in the unperturbed universe. This can be of serious consequences as a change of distance affects the mapping of CMB temperature fluctuations into the angular power spectrum. In addition, if the change of distance is relatively uniform no new temperature fluctuations are generated. It is therefore a different effect than the lensing or ISW effects which introduce additional CMB anisotropies. This paper shows that the accuracy of the CMB analysis can be impaired by the accuracy of calculation of the distance within the cosmological models. Since this effect has not been fully explored before, to test how the inhomogeneities affect the distance-redshift relation, several methods are examined: the Dyer-Roeder relation, lensing approximation, and non-linear Swiss-Cheese model. In all cases, the distance to the last scattering surface is different than when homogeneity is assumed. The difference can be as low as 1% and as high as 80%. Excluding extreme cases, the distance changes by about 20-30%. Since the distance to the last scattering surface is set by the position of the CMB peaks, in order to have a good fit, the distance needs to be adjusted. After correcting the distance, the cosmological parameters change. Therefore, a not properly estimated distance to the last scattering surface can be a major source of systematics. This paper shows that if inhomogeneities are taken into account when calculating the distance then models with positive spatial curvature and with \Omega_\Lambda ~ 0.8-0.9 are preferred. The \Lambda CDM model in most cases, is at odds with the current data.

Abstract: In this paper we investigate non-compact FRW type Kaluza-Klein cosmology coupled with 5D energy-momentum tensor. The field equations are solved by taking gravitational and cosmological constants as a function of time $t$. We use $\Lambda(t)=\epsilon H^{2}$ to explore cosmological parameters including statefinder and discuss them for dust, radiation and stiff matter dominated eras. Also, we evaluate lookback time, proper distance, luminosity distance and angular diameter distance. We obtain a universe which is not compatible with current cosmological observations at $\epsilon=6$. However, for $\epsilon>6$, the results are compatible with observational cosmology.

Abstract: In this paper we investigate non-compact FRW type Kaluza-Klein cosmology coupled with 5D energy-momentum tensor. The field equations are solved by taking gravitational and cosmological constants as a function of time t. We use Λ(t)=eH 2 to explore cosmological parameters including statefinder and discuss them for dust, radiation and stiff matter dominated eras. Also, we evaluate lookback time, proper distance, luminosity distance and angular diameter distance. We obtain a universe which is not compatible with current cosmological observations at e=6. However, for e>6, the results are compatible with observational cosmology.

Abstract: Galaxy clusters present unique advantages for cosmological study. Here we collect a new sample of 10 lensing galaxy clusters with X-ray observations to constrain cosmological parameters. The redshifts of the lensing clusters lie between 0.1 and 0.6, and the redshift range of their arcs is from 0.4 to 4.9. These clusters are selected carefully from strong gravitational lensing systems which have both X-ray satellite observations and optical giant luminous arcs with known redshifts. Giant arcs usually appear in the central region of clusters, where mass can be traced with luminosity quite well. Based on gravitational lensing theory and a cluster mass distribution model, we can derive a ratio using two angular diameter distances. One is the distance between lensing sources and the other is that between the deflector and the source. Since angular diameter distance relies heavily on cosmological geometry, we can use these ratios to constrain cosmological models. Moreover, X-ray gas fractions of galaxy clusters can also be a cosmological probe. Because there are a dozen parameters to be fitted, we introduce a new analytic algorithm, Powell’s UOBYQA (Unconstrained Optimization By Quadratic Approximation), to accelerate our calculation. Our result demonstrates that this algorithm is an effective fitting method for such a continuous multi-parameter constraint. We find an interesting fact that these two approaches are separately sensitive to Ω Λ and Ω M . By combining them, we can get reasonable fitting values of basic cosmological parameters: Ω M = 0.26 +0.04 −0.04 , and Ω Λ = 0.82 +0.14 −0.16 .

Abstract: We study the redshift drift, i.e., the time derivative of the cosmological redshift in the Lemaitre-Tolman-Bondi (LTB) solution in which the observer is assumed to be located at the symmetry center. This solution has often been studied as an anti-Copernican universe model to explain the acceleration of cosmic volume expansion without introducing the concept of dark energy. One of the decisive differences between LTB universe models and Copernican universe models with dark energy is believed to be the redshift drift. The redshift drift is negative in all known LTB universe models, whereas it is positive in the redshift domain z < or approx. 2 in Copernican models with dark energy. However, there have been no detailed studies on this subject. In the present paper, we prove that the redshift drift of an off-center source is always negative in the case of LTB void models. We also show that the redshift drift can be positive with an extremely large hump-type inhomogeneity. Our results suggest that we can determine whether we live near the center of a large void without dark energy by observing the redshift drift.

Abstract: Under certain general conditions in an expanding universe, the luminosity distance (${d}_{L}$) and angular diameter distance (${d}_{A}$) are connected by the Etherington relation as ${d}_{L}={d}_{A}(1+z{)}^{2}$. The Tolman test suggests the use of objects of known surface brightness, to test this relation. In this Letter, we propose the use of a redshifted 21 cm signal from disk galaxies, where neutral hydrogen (HI) masses are seen to be almost linearly correlated with surface area, to conduct a new Tolman test. We construct simulated catalogs of galaxies, with the observed size-luminosity relation and realistic redshift evolution of HI mass functions, likely to be detected with the planned Square Kilometer Array. We demonstrate that these observations may soon provide the best implementation of the Tolman test to detect any violation of the cosmic distance duality relation.

Abstract: Proposed space-based gravitational-wave detectors such as BBO and DECIGO can detect {approx}10{sup 6} neutron star (NS) binaries and determine the luminosity distance to the binaries with high precision. Combining the luminosity distance and electromagnetically derived redshift, one would be able to probe cosmological expansion out to high redshift. In this paper, we show that the Hubble parameter as a function of redshift can be directly measured with monopole and dipole components of the luminosity distance on the sky. As a result, the measurement accuracies of the Hubble parameter in each redshift bin up to z=1 are 3-14%, 1.5-8%, and 0.8-4% for the observation time 1 yr, 3 yr, and 10 yr, respectively.

Abstract: Aims. The small-scale nature of spacetime can be tested with observations of distant quasars. We comment on a recent paper by Tamburini et al. (A&A, 533, 71) which claims that Hubble Space Telescope observations of the most distant quasars place severe constraints on models of foamy spacetime. Methods. If space is foamy on the Planck scale, photons emitted from distant objects will accumulate uncertainties in distance and propagation directions thus affecting the expected angular size of a compact object as a function of redshift. We discuss the geometry of foamy spacetime, and the appropriate distance measure for calculating the expected angular broadening. We also address the mechanics of carrying out such a test. We draw upon our previously published work on this subject (Christiansen et al. 2011), which carried out similar tests as Tamburini et al. and also went considerably beyond their work in several respects. Results. When calculating the path taken by photons as they travel from a distant source to Earth, one must use the comoving distance rather than the luminosity distance. This then also becomes the appropriate distance to use when calculating the angular broadening expected in a distant source. The use of the wrong distance measure causes Tamburini et al. to overstate the constraints that can be placed on models of spacetime foam. In addition, we consider the impact of different ways of parametrizing and measuring the effects of spacetime foam. Given the variation of the shape of the point-spread function (PSF) on the chip, as well as observation-specific factors, it is important to select carefully -- and document -- the comparison stars used as well as the methods used to compute the Strehl ratio.