Abstract: 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.

Abstract: Strong lensing time-delay systems constrain cosmological parameters via the so-called time-delay distance and the angular diameter distance to the lens. In previous studies, only the former information was used. In this paper, we show that the cosmological constraints improve significantly when the latter information is also included. Specifically, the angular diameter distance plays a crucial role in breaking the degeneracy between the curvature of the Universe and the time-varying equation of state of dark energy. Using a mock sample of 55 bright quadruple lens systems based on expectations for ongoing/future imaging surveys, we find that adding the angular diameter distance information to the time-delay distance information and the cosmic microwave background data of Planck improves the constraint on the constant equation of state by 30%, on the time variation in the equation of state by a factor of two, and on the Hubble constant in the flat $\Lambda$CDM model by a factor of two. Therefore, previous forecasts for the statistical power of time-delay systems were significantly underestimated, i.e., time-delay systems are more powerful than previously appreciated.

Abstract: We consider a Swiss Cheese model with a random arrangement of Lema\^itre--Tolman--Bondi holes in $\Lambda$CDM cheese. We study two kinds of holes with radius $r_b=50 h^{-1}$Mpc, with either an underdense or an overdense centre, called the open and closed case, respectively. We calculate the effect of the holes on the temperature, angular diameter distance and, for the first time in Swiss Cheese models, shear of the CMB. We quantify the systematic shift of the mean and the statistical scatter, and calculate the power spectra. In the open case, the temperature power spectrum is three orders of magnitude below the linear ISW spectrum. It is sensitive to the details of the hole, in the closed case the amplitude is two orders of magnitude smaller. In contrast, the power spectra of the distance and shear are more robust, and agree with perturbation theory and previous Swiss Cheese results. We do not find a statistically significant mean shift in the sky average of the angular diameter distance, and obtain the 95\% limit $|\Delta D_A/\bar{D}_A|\lesssim10^{-4}$. We consider the argument that areas of spherical surfaces are nearly unaffected by perturbations, which is often invoked in light propagation calculations. The closed case is consistent with this at 1$\sigma$, whereas in the open case the probability is only 1.4%.

Abstract: An expression for the average redshift drift in a statistically homogeneous and isotropic dust universe is given. The expression takes the same form as the expression for the redshift drift in FLRW models. It is used for a proof-of-principle study of the effects of backreaction on redshift drift measurements by combining the expression with two-region models. The study shows that backreaction can lead to positive redshift drift at low redshifts, exemplifying that a positive redshift drift at low redshifts does not require dark energy. Moreover, the study illustrates that models without a dark energy component can have an average redshift drift observationally indistinguishable from that of the standard model according to the currently expected precision of ELT measurements. In an appendix, spherically symmetric solutions to Einstein's equations with inhomogeneous dark energy and matter are used to study deviations from the average redshift drift and effects of local voids.

Abstract: We study the physically self-bound cold dark matter halo distribution, which we associate with the massive galaxies within Horizon Run 3, to estimate the accuracy of the determination of the cosmological distance scale measured by the topology analysis. We apply the routine Contour 3D to the 108 Mock Survey of π steradians out to redshift z = 0.6, which effectively corresponds to the SDSS-III Baryon Oscillation Spectroscopic Survey (BOSS) survey, and compare the topology with that of a Gaussian random phase field. We find that given three separate smoothing lengths λ = 15, 21, and 34 h –1 Mpc, the least χ2 fit genus per unit volume (g) yields a 1.7% fractional uncertainty in smoothing length and angular diameter distance to z = 0.6. This is an improvement on former calibrations and presents an error estimate competitive with baryon acoustic oscillation scale techniques. We also present three-dimensional graphics of the Horizon Run 3 spherical mock survey to show a wealth of large-scale structures of the universe that are expected for surveys like BOSS.

Abstract: By using type Ia supernovae (SNIa) to provide the luminosity distance (LD) directly, which depends on the value of the Hubble constant $H_0= 100 h\; {\rm km\; s^{-1}\; Mpc^{-1}}$, and the angular diameter distance from galaxy clusters or baryon acoustic oscillations (BAOs) to give the derived LD according to the distance duality relation, we propose a model-independent method to determine $h$ from the fact that different observations should give the same LD at a given redshift. Combining the Sloan Digital Sky Survey II (SDSS-II) SNIa from the MLCS2k2 light curve fit and galaxy cluster data, we find that at the $1\sigma$ confidence level (CL), $h=0.5867\pm0.0303$ for the sample of the elliptical $\beta$ model for galaxy clusters, and $h=0.6199\pm0.0293$ for that of the spherical $\beta$ model. The former is smaller than the values from other observations, whereas the latter is consistent with the Planck result at the $2\sigma$ CL and agrees very well with the value reconstructed directly from the $H(z)$ data. With the SDSS-II SNIa and BAO measurements, a tighter constraint, $h=0.6683\pm0.0221$, is obtained. For comparison, we also consider the Union 2.1 SNIa from the SALT2 light curve fitting. The results from the Union 2.1 SNIa are slightly larger than those from the SDSS-II SNIa, and the Union 2.1 SNIa + BAOs give the tightest value. We find that the values from SNIa + BAOs are quite consistent with those from the Planck and the BAOs, as well as the local measurement from Cepheids and very-low-redshift SNIa.

Abstract: W e investigate anisotropic Bianchi Type III cosmological model with bulk viscosity in the presence of time-varying gravitational constant and cosmological constant . To get deterministic solution, the viscous coefficient of bulk viscous fluid is assumed to be power function of mass density. It is found that the cosmological constant is positive and a decreasing function of time. The expression for proper distance, luminosity distance, angular diameter distance, look back time and distance modulus curve are analyzed and also the distance modulus curve of derived model nearly matches with Supernova Ia (SN Ia) observations.

Abstract: We present our development of Zeldovich’s ideas for the measurement of the cosmological angular diameter distance (ADD) in the Friedmann Universe. We derive the general differential equation for the ADD measurement which is valid for an open, spatially flat, and closed universe, and for any stress energy tensor. We solve these equations in terms of quadratures in a form suitable for further numerical investigations for the present universe filled by radiation, (baryonic and dark) matter, and dark energy. We perform the numerical investigation in the absence of radiation, and we show the strong dependence ADD has on the filling of the cone of light rays (CLR). The difference of the empty and totally filled CLR may reach 600–700 Mps for a redshift of $$f\simeq 3$$ .

Abstract: Anisotropic measurements of the Baryon Acoustic Oscillation (BAO) feature within a galaxy survey enable joint inference about the Hubble parameter $H(z)$ and angular diameter distance $D_A(z)$. These measurements are typically obtained from moments of the measured 2-point clustering statistics, with respect to the cosine of the angle to the line of sight $\mu$. The position of the BAO features in each moment depends on a combination of $D_A(z)$ and $H(z)$, and measuring the positions in two or more moments breaks this parameter degeneracy. We derive analytic formulae for the parameter combinations measured from moments given by Legendre polynomials, power laws and top-hat Wedges in $\mu$, showing explicitly what is being measured by each in real-space for both the correlation function and power spectrum, and in redshift-space for the power spectrum. The large volume covered by modern galaxy samples means that the correlation function can be well approximated as having no correlations at different $\mu$ on the BAO scale, and that the errors on this scale are approximately independent of $\mu$. Using these approximations, we derive the information content of various moments. We show that measurements made using either the monopole and quadrupole, or the monopole and $\mu^2$ power-law moment, are optimal for anisotropic BAO measurements, in that they contain all of the available information using two moments, the minimal number required to measure both $H(z)$ and $D_A(z)$. We test our predictions using 600 mock galaxy samples, matched to the SDSS-III Baryon Oscillation Spectroscopic Survey CMASS sample, finding a good match to our analytic predictions. Our results should enable the optimal extraction of information from future galaxy surveys such as eBOSS, DESI and Euclid.

Abstract: We present our development of Zeldovich's ideas for the measurement of the cosmological angular diameter distance (ADD) in the Friedmann Universe. We derive the general differential equation for the ADD measurement which is valid for an open, spatially-flat and closed universe, and for any stress energy tensor. We solve the mentioned equations in terms of quadratures in a form suitable for further numerical investigations for the present universe filled by radiation, (baryonic and dark) matter and dark energy. We perform the numerical investigation in the absence of radiation, and show the strong dependence ADD on the filling of the cone of light rays (CLR). The difference of the empty and totally filled CLR may reach 600-700 Mps. for the redshift $f\simeq 3$.

Abstract: According to the formerly reported 4-D spherical model of the time and universe, factors affecting the redshift are discussed. In addition to the factor from the space expansion, two other factors derived from the light speed variation are proposed. One is the energy density factor of the wave medium, which was formerly reported to determine the light speed. The second is a newly proposed factor caused by the electromagnetic interaction of light with substances in the 3-D space. Subsequently the direct correlation of the light propagated distance with the redshift is given. Superimposed graphs of it on the real observed data from the Supernova Cosmology Project exhibited an excellent fit for a case that the current radius (equal to our observed time) of the universe is between 0.7 and 0.8 of its maximum. This could be an important ground for a possibility of the 4-D spherical model, which implies that the universe has been expanding at a constant speed by our observed time.

Abstract: We present a python package "ScalPy" for studying the late time scalar field cosmology for a wide variety of scalar field models, namely the quintessence, tachyon and Galileon model. The package solves the autonomous system of equations for power law and exponential potential. But it can be easily generalized to add more complicated potential. For completeness, we also include the standard parameterization for dark energy models, e.g. the $\Lambda$CDM, $w$CDM, $w_{0}w_{a}$CDM as well as the GCG parameterization. The package also solves the linear growth equation for matter perturbations on sub-horizon scales. All the important observables related to background universe as well as to the perturbed universe, e.g. luminosity distance ($D_{L}(z)$), angular diameter distance ($D_{A}(z)$), normalized Hubble parameter ($h(z)$), lookback time ($t_{L}$), equation of state for the dark energy ($w(z)$), growth rate ($f=\frac{d \ln\delta}{d \ln a}$), linear matter power spectra ($P(k)$), and its normalization $\sigma_{8}$ can be obtained from this package. The code is further integrated with the publicly available MCMC hammer "emcee" to constrain the different models using the presently available observational data. The code is available online at \url{this https URL}

Abstract: The dark energy model with EoS parameter is derived for hypersurface-homogenous space-time filled with perfect fluid source in the frame work of f ( R , T ) gravity (Harko et al., arXiv: 1104.2669v2 [gr-qc], 2011). To obtain a determinate solution, special law of variation for Hubble’s parameter proposed by Berman [(Nuvo Cimento B, 74,183(1983)] is used. We have also assumed that the scalar expansion is proportional to shear and the EoS parameter is proportional to skewness parameter. In fact, the possibility of reconstruction of the hypersurface-homogenous cosmology with an appropriate choice of a function f ( T ) has been proved in f ( R , T ) gravity. It is observed that the EoS parameter, skewness parameters in the model turn out to be functions of cosmic time. Some physical and kinematical properties of the model are also discussed. We have also discussed the well known astrophysical phenomena, namely, look-back time, proper distance, luminosity distance, angular diameter distance with redshift.

Abstract: This paper describes the detail calculations of expected redshift change in the galaxies’ or other distant objects’ light after a certain amount of time between observations has elapsed. The detection of this phenomenon has been proposed since the Hubble’s discovery of the galaxies’ redshift dependence on their distance from Earth and their significant recession velocities. Various astrophysicists have performed such calculations for several cosmological models of the Universe, but not for the model introduced by the author of this paper. This is now addressed in this publication.

Abstract: Interdependence of luminosity distance and angular diameter distance, shown by the distance duality relation (DDR) is very signicant in observational Cosmology. Any deviation from this relation highlights the

Abstract: The secular redshift drift is a potential measurement to directly probe the cosmic expansion. Previous study on the redshift drift mainly focused on the model-dependent simulation. Apparently, the physical insights on the redshift drift are very necessary. So in this paper, it is investigated using thermodynamics on the apparent, Hubble and event horizons. Thermodynamics could analytically present the model-independent upper bounds of redshift drift. For specific assumption on the cosmological parameters, we find that the thermodynamics bounds are nearly one order of magnitude larger than the expectation in standard ΛCDM model. We then examine ten observed redshift drift from Green Bank Telescope at redshift 0.09 < z < 0.69, and find that these observational results are inconsistent with the thermodynamics. The size of the errorbars on these measurements is about three orders of magnitude larger than the effect of thermodynamical bounds for the redshift drift. Obviously, we have not yet hit any instrumental systematics at the shift level of 1m s−1 yr−1.

Abstract: In this Letter, we describe a new method to use baryon acoustic oscillations (BAO) to derive a constraint on the possible variation of the speed of light. The method relies on the fact that there is a simple relation between the angular diameter distance (${D}_{A}$) maximum and the Hubble function ($H$) evaluated at the same maximum-condition redshift, which includes speed of light $c$. We note the close analogy of the BAO probe with a laboratory experiment: here we have ${D}_{A}$ which plays the role of a standard (cosmological) ruler, and ${H}^{\ensuremath{-}1}$, with the dimension of time, as a (cosmological) clock. We evaluate if current or future missions such as Euclid can be sensitive enough to detect any variation of $c$.

Abstract: The distance-redshift relation plays a fundamental role in constraining cosmological models In this paper, we show that measurements of positions and time delays of strongly lensed images of a background galaxy, as well as those of the velocity dispersion and mass profile of a lens galaxy, can be combined to extract the angular diameter distance of the lens galaxy Physically, as the velocity dispersion and the time delay give a gravitational potential (GM/r) and a mass (GM) of the lens, respectively, dividing them gives a physical size (r) of the lens Comparing the physical size with the image positions of a lensed galaxy gives the angular diameter distance to the lens A mismatch between the exact locations at which these measurements are made can be corrected by measuring a local slope of the mass profile We expand on the original idea put forward by Paraficz and Hjorth, who analyzed singular isothermal lenses, by allowing for an arbitrary slope of a power-law spherical mass density profile, an external convergence, and an anisotropic velocity dispersion We find that the effect of external convergence cancels out when dividing the time delays and velocity dispersion measurements We derive a formula for the uncertainty in the angular diameter distance in terms of the uncertainties in the observables As an application, we use two existing strong lens systems, B1608+656 (zL=06304) and RXJ1131−1231 (zL=0295), to show that the uncertainty in the inferred angular diameter distances is dominated by that in the velocity dispersion, σ2, and its anisotropy We find that the current data on these systems should yield about 16% uncertainty in DA per object This improves to 13% when we measure σ2 at the so-called sweet-spot radius Achieving 7% is possible if we can determine σ2 with 5% precision

Abstract: The interdependence of luminosity distance, $D_L$ and angular diameter distance, $D_A$ given by the distance duality relation (DDR) is very significant in observational cosmology. It is very closely tied with the temperature- redshift relation of Cosmic Microwave Background (CMB) radiation. Any deviation from $\eta(z)\equiv \frac{D_L}{D_A (1+z)^2} =1$ indicates a possible emergence of new physics. Our aim in this work is to check the consistency of these relations using a non-parametric regression method namely, LOESS with SIMEX. This technique avoids dependency on the cosmological model and works with a minimal set of assumptions. Further, to analyze the efficiency of the methodology, we simulate a dataset of $200$ points of $\eta (z)$ data based on a phenomenological model $\eta(z)= (1+z)^\epsilon$. The error on the simulated data points is obtained by using the temperature of CMB radiation at various redshifts. For testing the distance duality relation, we use the JLA SNe Ia data for luminosity distances, while the angular diameter distances are obtained from radio galaxies datasets. Since the DDR is linked with CMB temperature - redshift relation, therefore we also use the CMB temperature data to reconstruct $\eta (z)$. It is important to note that with CMB data, we are able to study the evolution of DDR up to a very high redshift $ z = 2.418$. In this analysis, we find no evidence of deviation from $\eta=1$ within a $1\sigma$ region in the entire redshift range used in this analysis ($0 < z \leq 2.418$).

Abstract: The cosmic expansion history is investigated from the distance indicator and secular redshift drift. Three types of classical kinematics deceleration parameters and jerk parameters are investigated using the redshift drift. They are also compared with the results from current and future type Ia supernova measurements. For the linear and nonlinear models, all these observations favor a recent accelerating expansion, and previous deceleration. In order to determine which kind of data can provide us a model-independent estimation on the cosmic expansion history, we give a method and find that the redshift drift is more stable to explore the expansion history than distance indicator. From the constraints on deceleration factor today q 0, we find that the future redshift drift also has the potential to test the slowing down of cosmic acceleration. For the piecewise model, we find that the redshift drift is more effective to express recent accelerating and previous decelerating expansion in the average sense.

Abstract: We propose and perform a new test of the cosmic distance-duality relation (CDDR), $D_L(z) / D_A(z) (1 + z)^{2} = 1$, where $D_A$ is the angular diameter distance and $D_L$ 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 $D=D_{A_{12}}/D_{A_2}$ and $D^{*}=D_{L_{12}}/D_{L_{2}}$, where the subscripts 1 and 2 correspond, respectively, to redshifts $z_1$ and $z_2$, are linked by $D/D^*=(1+z_1)^2$ if the CDDR is valid. We allow departures from the CDDR by defining two funcions for $\eta(z_1)$, 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 1$\sigma$ confidence level ($\eta(z) \simeq 1$), in complete agreement with other tests and reinforcing the theoretical pillars of the CDDR.

Abstract: Recent calculations using non-linear relativistic cosmological perturbation theory show biases in the mean luminosity distance and distance modulus at low redshift. We show that these effects may be understood very simply as a non-relativistic, and purely kinematic, Malmquist-like bias, and we describe how the effect changes if one averages over sources that are limited by apparent magnitude. This effect is essentially identical to the distance bias from small-scale random velocities that has previously been considered by astronomers, though we find that the standard formula overestimates the homogeneous bias by a factor 2.

Abstract: Author(s): Zhu, F; Padmanabhan, N; White, M | Abstract: Future baryon acoustic oscillation (BAO) surveys will survey very large volumes, covering wide ranges in redshift. We derive a set of redshift weights to compress the information in the redshift direction to a small number of modes. We suggest that such a compression preserves almost all of the signal for most cosmologies, while giving high signal-to-noise measurements for each combination. We present some toy models and simple worked examples. As an intermediate step, we give a precise meaning to the 'effective redshift' of a BAO measurement.

Abstract: A check of the validity of the distance-duality relation (DDR) is necessary since a violation of one of the assumptions underlying this relation might be possible. In this paper, we test the DDR by combining the Union2.1 type Ia supernovae (SNIa) and five angular diameter distance data from the baryonic acoustic oscillation (BAO) measurements. We find that the DDR is consistent with the observations at the $2\ensuremath{\sigma}$ confidence level (CL) for the case of the Hubble constant $h=0.7$, and the consistency is improved to be $1\ensuremath{\sigma}$ CL when $h=0.7$ is replaced by the latest constraint from the Planck satellite, i.e., $h=0.678$, or $h$ is marginalized. Our results show that the BAO measurement is a very powerful tool to test the DDR. With more and more BAO data being released in the future, we are expecting a better validity check of the DDR.