Distance Duality Research Articles

An opacity-free method of testing the cosmic distance duality relation using strongly lensed gravitational wave signals

An opacity-free method of testing the cosmic distance duality relation using strongly lensed gravitational wave signals

Model - Independent Probe of Cosmic Distance Duality Relation

Abstract In this paper, cosmic distance duality relation is probed without considering any background cosmological model. The only \textit{a priori} assumption is that the Universe is described by the Friedmann-Lema$\hat{i}$tre-Robertson-Walker (FLRW) metric 
The strong gravitational lensing (SGL) data is used to construct the dimensionless co-moving distance function $d(z)$ and latest type Ia supernovae (SNe Ia) Pantheon+ data is used to estimate luminosity distances at the corresponding redshifts $z$. Using the distance sum rule along null geodesics of the FLRW metric, the CDDR violation is probed in both flat and non-flat space-time by considering two parametrizations for $\eta(z)$, the function generally used to probe the possible deviations from CDDR. The results show that, CDDR is compatible with the observations at a very high level of confidence for linear parametrization in flat Universe. In non-flat Universe too, CDDR is valid within $1\sigma$ confidence interval with a mild dependence of $\eta$ on the curvature density parameter $\Omega_{K}$ . The results for non-linear parametrization also show no significant deviation from CDDR.

Testing the Cosmic Distance Duality Relation Using Strong Gravitational Lensing Time Delays and Type Ia Supernovae

Abstract We present a comprehensive test of the cosmic distance duality relation (DDR) using a combination of strong gravitational lensing (SGL) time delay measurements and Type Ia supernovae (SNe Ia) data. We investigate three different parameterizations of potential DDR violations. To bridge the gap between SGL and SNe Ia data sets, we implement an artificial neural network approach to reconstruct the distance modulus of SNe Ia. Our analysis uniquely considers both scenarios where the absolute magnitude of SNe Ia (M B ) is treated as a free parameter and where it is fixed to a Cepheid-calibrated value. Using a sample of six SGL systems and the Pantheon+ SNe Ia data set, we find no statistically significant evidence for DDR violations across all parameterizations. The consistency of our findings across different parameterizations not only reinforces confidence in the standard DDR but also demonstrates the robustness of our analytical approach.

High-redshift cosmography with a possible cosmic distance duality relation violation

In this study, we used geometric distances at high redshifts (both luminosity and angular) to perform a cosmographic analysis with the Padé method, which stabilizes the behaviour of the cosmographic series in this redshift regime. However, in our analyses, we did not assume the validity of the Cosmic Distance Duality Relation (CDDR), but allowed for potential violations, such as d L (z) = η(z)(1+z)2 d A (z), where three different functional forms of η(z) are considered. By incorporating updated data from supernovae (SN), baryon acoustic oscillations (BAO), and cosmic chronometers (CC), we obtained observational constraints on cosmographic models alongside possible CDDR violations. Interestingly, we found that potential CDDR violations introduce new statistical correlations among cosmographic parameters such as H 0, q 0, and j 0. Nonetheless, within this framework, we did not observe significant deviations from the CDDR, and our results remain consistent with the predictions of the ΛCDM model. In the same time, this work provides a novel and straightforward method for testing the CDDR by fixing the background evolution through cosmographic techniques, paving the way for new geometric observational tests of possible deviations from standard cosmology.

Cosmic distance duality relation in light of time-delayed strong gravitational lensing* *Supported by the National Natural Science Fund of China (12275034, 12347101) and the Fundamental Research Funds for the Central Universities of China (2024CDJXY-022)

The cosmic distance duality relation (DDR), which links the angular-diameter and luminosity distances, is a cornerstone in modern cosmology. Any deviation from DDR may indicate new physics beyond the standard cosmological model. In this study, we used four high-precision time-delayed strong gravitational lensing (SGL) systems provided by H0LiCOW to test the validity of DDR. To this end, we directly compared the angular-diameter distances from these SGL systems with the luminosity distances from the latest Pantheon+ compilation of SNe Ia. To reduce the statistical errors arising from redshift matching, a Gaussian process method was applied to reconstruct the distance-redshift relation from the Pantheon+ dataset. We parameterized the possible violation of DDR in three different models. All results confirm the validity of DDR at confidence level. Additionally, Monte Carlo simulations based on the future LSST survey indicated that the precision of DDR could reach the level with 100 SGL systems.

Unveiling the Hubble constant through galaxy cluster gas mass fractions

In this work, we obtain Hubble constant (H0) estimates by using two galaxy cluster gas mass fraction measurement samples, Type Ia supernovae luminosity distances, and the validity of the cosmic distance duality relation. Notably, the angular diameter distance (ADD) to each galaxy cluster in the samples is determined by combining its gas mass fraction measurement with galaxy clustering observations, more precisely, the Ωb/Ωm ratio. Such a combination results in a H0 estimate that is independent of a specific cosmological framework. In one of the samples, the gas fraction measurements were calculated in spherical shells at radii near r2500 (44 data points), while in the other (103 data points) the measurements were calculated within r500. We find H0=72.7−5.6+6.3 km/s/Mpc at 68% CL for the joint analysis of these data sets. We also investigate the impact on the H0 determination by exploring the precision and number of gas mass fraction data by performing a data Monte Carlo simulation. Our simulations show that future measurements could achieve a precision of up to 5% for H0.

Testing the cosmic distance duality relation with Type Ia supernova and transverse BAO measurements

In this work, we test the cosmic distance duality relation (CDDR) by comparing the angular diameter distance (ADD) derived from the transverse Baryon Acoustic Oscillations (BAO) data with the luminosity distance (LD) from the Pantheon type Ia supernova (SNIa) sample. The binning method and Gaussian process are employed to match ADD data with LD data at the same redshift. First, we use nonparametric and parametric methods to investigate the impact of the specific prior values of the absolute magnitude MB\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$M_\ extrm{B}$$\\end{document} from SNIa observations and the sound horizon scale rs\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$r_\ extrm{s}$$\\end{document} from transverse BAO measurements on the CDDR tests. The results obtained from the parametric and non-parametric methods indicate that specific prior values of MB\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$M_\ extrm{B}$$\\end{document} and rs\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$r_\ extrm{s}$$\\end{document} lead to significant biases on the CDDR test. Then, to avoid these biases, we propose a method independent of MB\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$M_\ extrm{B}$$\\end{document} and rs\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$r_\ extrm{s}$$\\end{document} to test CDDR by considering the fiducial value of κ≡10MB5rs\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\kappa \\equiv 10^{M_\ extrm{B} \\over 5}r_\ extrm{s}$$\\end{document} as a nuisance parameter and then marginalizing its influence with a flat prior in the analysis. No violation of the CDDR is found, and the transverse BAO measurement can be used as a powerful tool to verify the validity of CDDR in the cosmological-model-independent method.

A Hubble constant estimate from galaxy cluster and type Ia SNe observations

In this work, we constrain the Hubble constant parameter, H 0, using a combination of the Pantheon sample and galaxy clusters (GC) measurements from minimal cosmological assumptions. Assuming the validity of the cosmic distance duality relation, an estimator is created for H 0 that only depends on simple geometrical distances, which is evaluated from Pantheon and a GC angular diameter distance sample afterward. The statistical and systematic errors in GC measurements are summed in quadrature in our analysis. We find H 0 = 67.22 ± 6.07 km s-1 Mpc-1 in 1σ confidence level (C.L.). This measurement presents an error of around 9%, showing that future and better GC measurements can shed light on the current Hubble tension.

Measurements of the Hubble constant from combinations of supernovae and radio quasars

In this letter, we propose an improved cosmological model independent method of determining the value of the Hubble constant H0. The method uses unanchored luminosity distances H0dL(z) from SN Ia Pantheon data combined with angular diameter distances dA(z) from a sample of intermediate luminosity radio quasars calibrated as standard rulers. The distance duality relation between dL(z) and dA(z), which is robust and independent of any cosmological model, allows to disentangle H0 from such combination. However, the number of redshift matched quasars and SN Ia pairs is small (37 data-points). Hence, we take an advantage from the Artificial Neural Network (ANN) method to recover the dA(z) relation from a network trained on full 120 radio quasar sample. In this case, the result is unambiguously consistent with values of H0 obtained from local probes by SH0ES and H0LiCOW collaborations. Three statistical summary measures: weighted mean H˜0=73.51(±0.67) km s−1 Mpc−1, median Med(H0)=74.71(±4.08) km s−1 Mpc−1 and MCMC simulated posterior distribution H0=73.52−0.68+0.66 km s−1 Mpc−1 are fully consistent with each other and the precision reached 1% level. This is encouraging for the future applications of our method. Because individual measurements of H0 are related to different redshifts spanning the range z=0.5−2.0, we take advantage of this fact to check if there is any noticeable trend in H0 measurements with redshift of objects used for this purpose. However, our result is that the data we used strongly support the lack of such systematic effects.

Distance Duality Test: The Evolution of Radio Sources Mimics a Nonexpanding Universe

Distance duality relation (DDR) marks a fundamental difference between expanding and nonexpanding universes, as an expanding metric causes angular diameter distance smaller than luminosity distance by an extra factor of (1 + z). Here we report a test of this relation using two independent samples of ultracompact radio sources observed at 2.29 GHz and 5.0 GHz. The test with radio sources involves only geometry, so it is independent of cosmological models. Since the observed radio luminosities systematically increase with redshift, we do not assume a constant source size. Instead, we start with assuming the intensive property, luminosity density, does not evolve with redshift and then infer its evolution from the resultant DDR. We make the same assumption for both samples, and find it results in the same angular size–redshift relation. Interestingly, the resultant DDR is fully consistent with a nonexpanding universe. Imposing the DDR predicted by the expanding universe, we infer the radio luminosity density evolves as ρ L ∝ (1 + z)3. However, the perfect agreement with a nonexpanding universe under the assumption of constant luminosity densities poses a conspiracy and fine-tuning problem: the size and luminosity density of ultracompact radio sources evolve in the way that precisely mimics a nonexpanding universe.

The Hubble constant from galaxy cluster scaling-relation and SNe Ia observations: a consistency test

In this paper, we propose a self-consistent test for a Hubble constant estimate using galaxy cluster and type Ia supernovae (SNe Ia) observations. The approach consists, in a first step, of obtaining the observational value of the galaxy cluster scaling-relation Y_{SZE}D_{A}^{2}/C_{XSZ}Y_X = C by combining the X-Ray and SZ observations of galaxy clusters at low redshifts (z < 0.1) from the first Planck mission all-sky data set (0.044 le z le 0.444), along with SNe Ia observations and making use of the cosmic distance duality relation validity. Then, by considering a flat Lambda CDM model for D_A, the constant C from the first step and the Planck prior on Omega _M parameter, we obtain H_0 by using the galaxy cluster data with z>0.1. As a result, we obtain { H_0=73.014^{+7.435}_{-6.688}} km/s/Mpc, in full agreement with the latest results from HST + SH0ES team. We also compare our method with that one where the C parameter is obtained from hydrodynamical simulations of massive galaxy clusters.

Testing cosmology with double source lensing

Double source lensing provides a dimensionless ratio ofdistance ratios, a “remote viewing” of cosmology throughdistances relative to the gravitational lens, beyond theobserver. We use this to test the cosmological framework,particularly with respect to spatial curvature and thedistance duality relation. We derive a consistency equationfor constant spatial curvature, allowing not only theinvestigation of flat vs curved but of theFriedmann-Lemaître-Robertson-Walker framework itself.For distance duality, we demonstrate that the evolution ofthe lens mass profile slope must becontrolled to ≳ 5 times tighter fractional precisionthan a claimed distance duality violation.Using LensPop forecasts of double source lensingsystems in Euclid and LSST surveys we also explore constraintson dark energy equation of state parameters and anyevolution of the lens mass profile slope.

Hubble speed from first principles

We introduce a way of measuring ${H}_{0}$ from a combination of independent geometrical data sets, without the need for calibration or the choice of a cosmological model. We build on the distance duality relation, which sets the ratio of the luminosity and angular diameter distance to a fixed scaling in redshift for any metric theory of gravity with standard photon propagation and constitutes a founding block of any theory describing our Universe. Our method allows us to determine ${H}_{0}$ from first principles, unleashing the measurement of this fundamental constant from calibration and the assumption of a cosmological model. We find ${H}_{0}=69.5\ifmmode\pm\else\textpm\fi{}1.7\text{ }\text{ }\mathrm{km}/\mathrm{s}/\mathrm{Mpc}$ at 68% C.L., showing that the Hubble constant can be constrained at the percent level with minimal assumptions.

What are recent observations telling us in light of improved tests of distance duality relation?

As an exact result required by the Etherington reciprocity theorem, the cosmic distance duality relation (CDDR), η(z)=DL(z)(1+z)−2/DA(z)=1 plays an essential part in modern cosmology. In this paper, we present a new method (η(zi)/η(zj)) to use the measurements of ultra-compact structure in radio quasars (QSO) and the latest observations of type Ia supernova (SN Ia) to test CDDR. By taking the observations directly from SN Ia and QSOs, one can completely eliminate the uncertainty caused by the calibration of the absolute magnitudes of standard candles (MB) and the linear sizes of standard rulers (lm). Benefit from the absence of nuisance parameters involved in other currently available methods, our analysis demonstrates no evidence for the deviation and redshift evolution of CDDR up to z=2.3. The combination of our methodology and the machine learning Artificial Neural Network (ANN) would produce 10−3 level constraints on the violation parameter at high redshifts. Our results indicate perfect agreement between observations and predictions, supporting the persisting claims that the Etherington reciprocity theorem could still be the best description of our universe.

Etherington duality breaking: gravitational lensing in non-metric space–times versus intrinsic alignments

ABSTRACT The Etherington distance duality relation is well-established for metric theories of gravity, and confirms the duality between the luminosity distance and the angular diameter distance through the conservation of surface brightness. A violation of the Etherington distance duality due to lensing in a non-metric space–time would lead to fluctuations in surface brightness of galaxies. Likewise, fluctuations of the surface brightness can arise in classical astrophysics as a consequence of intrinsic tidal interaction of galaxies with their environment. Therefore, we study these in two cases in detail: First, for intrinsic size fluctuations and the resulting changes in surface brightness, and secondly, for an area-metric space–time as an example of a non-metric space–time, where the distance duality relation itself acquires modifications. The aim of this work is to quantify whether a surface brightness fluctuation effect due to area-metric gravity would be resolvable compared to the similar effect caused by intrinsic alignment. We thus compare the auto- and cross-correlations of the angular spectra in these two cases and show that the fluctuations in intrinsic brightness can potentially be measured with a cumulative signal-to-noise ratio Σ(ℓ) ≥ 3 in a Euclid-like survey. The measurement in area-metric space–times, however, depends on the specific parameter choices, which also determine the shape and amplitude of the spectra. While lensing surveys do have sensitivity to lensing-induced surface brightness fluctuations in area-metric space–times, the measurement does not seem to be possible for natural values of the Etherington-breaking parameters.

Model-independent Test for the Cosmic Distance–Duality Relation with Pantheon and eBOSS DR16 Quasar Sample

In this Paper, we carry out a new model-independent cosmological test for the cosmic distance–duality relation (CDDR) by combining the latest five baryon acoustic oscillation (BAO) measurements and the Pantheon type Ia supernova (SNIa) sample. Particularly, the BAO measurement from the extended Baryon Oscillation Spectroscopic Survey data release 16 quasar sample at effective redshift z = 1.48 is used, and two methods, i.e., a compressed form of the Pantheon sample and the artificial neural network combined with the binning SNIa method, are applied to overcome the redshift-matching problem. Our results suggest that the CDDR is compatible with the observations, and the high-redshift BAO and SNIa data can effectively strengthen the constraints on the violation parameters of CDDR with the confidence interval decreasing by more than 20%. In addition, we find that the compressed form of observational data can provide a more rigorous constraint on the CDDR, and thus can be generalized to the applications of other actual observational data with limited sample size in the test for CDDR.

Deep learning method for testing the cosmic distance duality relation* *Supported by the National Natural Science Fund of China (11873001 and 12147102), and the Fundamental Research Funds for the Central Universities of China (2022CDJXY-002)

The cosmic distance duality relation (DDR) is constrained by a combination of type-Ia supernovae (SNe Ia) and strong gravitational lensing (SGL) systems using the deep learning method. To make use of the full SGL data, we reconstruct the luminosity distance from SNe Ia up to the highest redshift of SGL using deep learning, and then, this luminosity distance is compared with the angular diameter distance obtained from SGL. Considering the influence of the lens mass profile, we constrain the possible violation of the DDR in three lens mass models. The results show that, in the singular isothermal sphere and extended power-law models, the DDR is violated at a high confidence level, with the violation parameter and , respectively. In the power-law model, however, the DDR is verified within a 1σ confidence level, with the violation parameter . Our results demonstrate that the constraints on the DDR strongly depend on the lens mass models. Given a specific lens mass model, the DDR can be constrained at a precision of using deep learning.

First-order methods for the convex hull membership problem

The convex hull membership problem (CHMP) consists in deciding whether a certain point belongs to the convex hull of a finite set of points, a decision problem with important applications in computational geometry and in foundations of linear programming. In this study, we review, compare and analyze first-order methods for CHMP, namely, Frank-Wolfe type methods, Projected Gradient methods and a recently introduced geometric algorithm, called Triangle Algorithm (TA). We discuss the connections between this algorithm and Frank-Wolfe, showing that TA can be interpreted as an inexact Frank-Wolfe. Despite this similarity, TA is strongly based on a theorem of alternatives known as distance duality. By using this theorem, we propose suitable stopping criteria for CHMP to be integrated into Frank-Wolfe type and Projected Gradient, specializing these methods to the membership decision problem. Interestingly, Frank-Wolfe integrated with such stopping criteria coincides with a greedy version of the Triangle Algorithm which is, in its turn, equivalent to an algorithm due to von Neumann. We report numerical experiments on random instances of CHMP, carefully designed to cover different scenarios, that indicate which algorithm is preferable according to the geometry of the convex hull and the relative position of the query point. Concerning potential applications, we present two illustrative examples, one related to linear programming feasibility problems and another related to image classification problems.

Cosmological-model-independent tests of cosmic distance duality relation with Type Ia supernovae and radio quasars

In this paper, we investigate the possible deviations of the cosmic distance duality relation (CDDR) using the combination of the largest SNe Ia (Pantheon) and compact radio quasar (QSO) samples through two model-independent approaches. The deviation of CDDR is written as DL(z)/DA(z)(1+z)−2=η(z) and η(z)=eτ(z)/2, with the parameterizations of F1 (τ(z)=2ϵ1z) and F2 (τ(z)=(1+z)2ϵ2−1). Furthermore, in order to compare the two resulting distances, two cosmological-model-independent methods, i.e., the nearby SNe Ia method and the GP method are employed to match the two distinct data at the same redshift. Our findings indicate that, compared with the results obtained in the literature, there is an improvement in precision when the latest SNe Ia and QSO samples are used. Specially, in the framework of nearby SNe Ia method, the CDDR would be constrained at the precision of Δϵ1=0.013 in Model F1 and Δϵ2=0.018 in Model F2. Regarding the GP method, one observes that a larger data size would produce more stringent constraints on the CDDR parameters. Therefore, accompanied by further developments in cosmological observations and the analysis methods, our analysis provides an insight into the evidence for unaccounted opacity sources at an earlier stage of the universe, or at the very least the new physics involved.

A test of the evolution of gas depletion factor in galaxy clusters using strong gravitational lensing systems

In this work, we discuss a new method to probe the redshift evolution of the gas depletion factor, i.e. the ratio by which the gas mass fraction of galaxy clusters is depleted with respect to the universal mean of baryon fraction. The dataset we use for this purpose consists of 40 gas mass fraction measurements measured at r_{2500} using Chandra X-ray observations, strong gravitational lensing sub-samples obtained from SLOAN Lens ACS + BOSS Emission-line Lens Survey (BELLS) + Strong Legacy Survey SL2S + SLACS. For our analysis, the validity of the cosmic distance duality relation is assumed. We find a mildly decreasing trend for the gas depletion factor as a function of redshift at about 2.7sigma .