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 forecasting cosmographic constraints. 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 Planck's measurements of the cosmic microwave background anisotropies 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 ΛCDM model by a factor of two. Therefore, previous forecasts for the statistical power of time-delay systems were overly pessimistic, i.e., time-delay systems are more powerful than previously appreciated.

Abstract: How does inhomogeneity affect our interpretation of cosmological observations? It has long been wondered to what extent the observable properties of an inhomogeneous universe differ from those of a corresponding Friedmann?Lema?tre?Robertson?Walker (FLRW) model, and how the inhomogeneities affect that correspondence. Here, we use numerical relativity to study the behavior of light beams traversing an inhomogeneous universe, and construct the resulting Hubble diagrams. The universe that emerges exhibits an average FLRW behavior, but inhomogeneous structures contribute to deviations in observables across the observer's sky. We also investigate the relationship between angular diameter distance and the angular extent of a source, finding deviations that grow with source redshift. These departures from FLRW are important path-dependent effects, with implications for using real observables in an inhomogeneous universe such as our own.

Abstract: 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=DA12/DA2 and D*=DL12/DL2, 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.

Abstract: We propose a new model-independent method to test the cosmic curvature by comparing the proper distance and transverse comoving distance. Using the measurements of Hubble parameter $H(z)$ and angular diameter distance $d_A$, the cosmic curvature parameter $\Omega_K$ is constrained to be $-0.09\pm0.19$, which is consistent with a flat universe. We also use Monte Carlo simulation to test the validity and efficiency, and find that our method can give a reliable and efficient constraint on cosmic curvature. Compared with other model-independent methods testing the cosmic curvature, our method can avoid some drawbacks and give a better constraint.

Abstract: The recent analysis of low-redshift supernovae (SN) has increased the apparent tension between the value of $H_0$ estimated from low and high redshift observations such as the cosmic microwave background (CMB) radiation. At the same time other observations have provided evidence of the existence of local radial inhomogeneities extending in different directions up to a redshift of about $0.07$. About $40\%$ of the Cepheids used for SN calibration are directly affected because are located along the directions of these inhomogeneities. We derive a new simple formula relating directly the luminosity distance to the monopole of the density contrast, which does not involve any metric perturbation. We then use it to develop a new inversion method to reconstruct the monopole of the density field from the deviations of the redshift uncorrected observed luminosity distance respect to the $\Lambda CDM$ prediction based on cosmological parameters obtained from large scale observations. The inversion method confirms the existence of inhomogeneities whose effects were not previously taken into account because the $2M++$ density field maps used to obtain the peculiar velocity for redshift correction were for $z\leq 0.06$, which is not a sufficiently large scale to detect the presence of inhomogeneities extending up to $z=0.07$. The inhomogeneity does not affect the high redshift luminosity distance because the volume averaged density contrast tends to zero asymptotically, making the value of $H_0^{CMB}$ obtained from CMB observations insensitive to any local structure. The inversion method can provide a unique tool to reconstruct the density field at high redshift where only SN data is available, and in particular to normalize correctly the density field respect to the average large scale density of the Universe.

Abstract: As is well known, measurements of the Sunyaev-Zeldovich effect can be combined with observations of the X-ray surface brightness of galaxy clusters to estimate the angular diameter distance to these structures. In this paper, we show that this technique depends on the fine structure constant, α. Therefore, if α is a time-dependent quantity, e.g., α = α0(z), where is a function of redshift, we argue that current data do not provide the real angular diameter distance, DA(z), to the cluster, but instead DAdata(z) = (z)2 DA(z). We use this result to derive constraints on a possible variation of α for a class of dilaton runaway models considering a sample of 25 measurements of DAdata(z) in redshift range 0.023 < z < 0.784 and estimates of DA(z) from current type Ia supernovae observations. We find no significant indication of variation of α with the present data.

Abstract: The interdependence of luminosity distance, DL and angular diameter distance, DA 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 η(z)≡ DL/DA (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 020 points of η (z) data based on a phenomenological model η(z)= (1+z). 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 η (z). It is important to note that with CMB data, we are able to study the evolution of DDR upto a very high redshift z = 2.418. In this analysis, we find no evidence of deviation from η=1 within a 1σ region in the entire redshift range used in this analysis (0 < z ≤ 2.418).

Abstract: The Etherington distance duality relation, which relates the luminosity distance, the angular diameter distance and the redshift of objects, depends only upon a conservation law for light that traces back directly to the Lorentzian spacetime geometry. We show that this duality relation indeed survives transition to the most general linear electrodynamics without birefringence, which rests on a spacetime geometry constituted by a Lorentzian metric and two scalar fields, a dilaton and an axion. By computing the Poynting vector and optical scalar transport in the geometrical optics limit of this framework, we derive the modification of the light flux in the presence of a dilaton field and present improved constraints on the gradient of the dilaton field from observations of the Cosmic Microwave Background spectrum. Although this flux modification may seem applicable also to fundamental modifications of the Etherington relation, we show that the distance duality relation still holds true. Thus any deviations within this classical theory would imply non-metricities, once astrophysical sources for attenuation, such as dust, are accounted for. Moreover, using the most up-to-date measurements of the luminosity distances to Supernovae of Type Ia, and the inferred angular diameter distances from the baryon acoustic feature measurements, we perform a scale-free and nearly model-independent test of the Etherington distance duality relation between redshifts of $0.38$ and $0.61$. We find consistency with the standard distance duality relation and constrain the optical depth of light between these two redshifts to $\Delta\tau=-0.006\pm0.046$.

Abstract: We propose a new model-independent method to test the cosmic curvature by comparing the proper distance and transverse comoving distance. Using the measurements of Hubble parameter $H(z)$ and angular diameter distance $d_A$, the cosmic curvature parameter $\Omega_K$ is constrained to be $-0.09\pm0.19$, which is consistent with a flat universe. We also use Monte Carlo simulation to test the validity and efficiency, and find that our method can give a reliable and efficient constraint on cosmic curvature. Compared with other model-independent methods testing the cosmic curvature, our method can avoid some drawbacks and give a better constraint.

Abstract: Based on optical imaging and spectroscopy of the Type II-Plateau SN 2013eq, we present a comparative study of commonly used distance determination methods based on Type II supernovae. The occurrence of SN 2013eq in the Hubble flow (z = 0.041 +/- 0.001) prompted us to investigate the implications of the difference between "angular" and "luminosity" distances within the framework of the expanding photosphere method (EPM) that relies upon a relation between flux and angular size to yield a distance. Following a re-derivation of the basic equations of the EPM for SNe at non-negligible redshifts, we conclude that the EPM results in an angular distance. The observed flux should be converted into the SN rest frame and the angular size, theta, has to be corrected by a factor of (1+z)^2. Alternatively, the EPM angular distance can be converted to a luminosity distance by implementing a modification of the angular size. For SN 2013eq, we find EPM luminosity distances of D_L = 151 +/- 18 Mpc and D_L = 164 +/- 20 Mpc by making use of different sets of dilution factors taken from the literature. Application of the standardized candle method for Type II-P SNe results in an independent luminosity distance estimate (D_L = 168 +/- 16 Mpc) that is consistent with the EPM estimate.

Abstract: Using the focusing equation, the equation for the cosmological angular diameter distance is derived, based on the ideas of Academician Ya.B. Zel'dovich, namely, that the distribution of matter at small angles is not homogeneous, and the light cone is close to being empty. We propose some ways of testing a method for measuring the angular diameter distances and show that the proposed method leads to results that agree better with the experimental data than those obtained by the usual methods.

Abstract: Using the Newman and Penrose spin coefficient (NP) formalism, we provide a derivation of the Dyer-Roeder equation for the angular diameter distance in cosmological space-times. We show that the geodesic deviation equation written in NP formalism is precisely the Dyer-Roeder equation for a general Friedman-Robertson-Walker (FRW) space-time, and then we examine the angular diameter distance to redshift relation in the case that a flat FRW metric is perturbed by a gravitational potential. We examine the perturbation in the case that the gravitational potential exhibits the properties of a thin gravitational lens, demonstrating how the weak lensing shear and convergence act as source terms for the perturbed Dyer-Roeder equation.

Abstract: In this paper we extend a new method to measure possible variation of the speed of light by using Baryon Acoustic Oscillations and the Hubble function presented in our earlier paper [V. Salzano, M. P. Dcabrowski, and R. Lazkoz, Phys. Rev. D93, 063521 (2016)] onto an inhomogeneous model of the universe. 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 $c$. One limit of such method was the assumption of null spatial curvature (even if we showed that even a non-zero curvature would have negligible effects). Here, we move one step further: we explicitly assume a model with intrinsic non-null curvature, and calculate the exact relation between $D_{A}$ and $H$ in this case. Then, we evaluate if current or future missions such as SKA can be sensitive enough to detect any such kind of spatial variation of $c$ which can perhaps be related to the recently observed spatial variation of the fine structure constant (an effect known as $\alpha$-dipole).

Abstract: Inspired by the string axiverse idea, it has been suggested that the recent transition from decelerated to accelerated cosmic expansion is driven by an axion-like quintessence field with a sub-Planckian decay constant. The scenario requires that the axion field be rather near the maximum of its potential, but is less finely tuned than other explanations of cosmic acceleration. The model is parametrized by an axion decay constant $f$, the axion mass $m$, and an initial misalignment angle $|\theta_i|$ which is close to $\pi$. In order to determine the $m$ and $\theta_{i}$ values consistent with observations, these parameters are mapped onto observables: the Hubble parameter $H(z)$ at and angular diameter distance $d_{A}(z)$ to redshift $z= 0.57$, as well as the angular sound horizon of the cosmic microwave background (CMB). Measurements of the baryon acoustic oscillation (BAO) scale at $z\simeq 0.57$ by the BOSS survey and Planck measurements of CMB temperature anisotropies are then used to probe the $\left\{m,f,\theta_i\right\}$ parameter space. With current data, CMB constraints are the most powerful, allowing a fraction of only $\sim 0.2$ of the parameter-space volume. Measurements of the BAO scale made using the SPHEREx or SKA experiments could go further, observationally distinguishing all but $\sim 10^{-2}$ or $\sim 10^{-5}$ of the parameter-space volume (allowed by simple priors) from the $\Lambda$CDM model.

Abstract: We discuss how the redshift (Mattig) method in Friedmann cosmology relates to dynamical distance indicators based on Newton's gravity (Teerikorpi 2011). It belongs to the class of indicators where the relevant length inside the system is the distance itself (in this case the proper metric distance). As the Friedmann model has Newtonian analogy, its use to infer distances has instructive similarities to classical dynamical distance indicators. In view of the theoretical exact linear distance-velocity law, we emphasize that it is conceptually correct to derive the cosmological distance via the route: redshift (primarily observed) --> space expansion velocity (not directly observed) --> metric distance (physical length in "cm"). Important properties of the proper metric distance are summarized.

Abstract: The redshift drift of objects moving in the Hubble flow has been proposed as a powerful model-independent probe of the underlying cosmology. A measurement of the first and second order redshift derivatives appears to be well within the reach of upcoming surveys using ELT-HIRES and the SKA Phase 2 array. Here we show that an unambiguous prediction of the R_h=ct cosmology is zero drift at all redshifts, contrasting sharply with all other models in which the expansion rate is variable. For example, multi-year monitoring of sources at redshift z=5 with the ELT-HIRES is expected to show a velocity shift Delta v = -15 cm/s/yr due to the redshift drift in Planck LCDM, while Delta v=0 cm/s/yr in R_h=ct. With an anticipated ELT-HIRES measurement error of +/-5 cm/s/yr after 5 years, these upcoming redshift drift measurements might therefore be able to differentiate between R_h=ct and Planck LCDM at ~3 sigma, assuming that any possible source evolution is well understood. Such a result would provide the strongest evidence yet in favour of the R_h=ct cosmology. With a 20-year baseline, these observations could favor one of these models over the other at better than 5 sigma.