Model-independent Test of the Cosmic Distance Duality Relation

Abstract

A validation of the cosmic distance duality (CDD) relation, η(z) ≡ (1+z) 2 d A (z)/d L (z) = 1, coupling the luminosity (d L ) and angular-diameter (d A ) distances, is crucial because its violation would require exotic new physics. We present a model-independent test of the CDD, based on strong lensing and a reconstruction of the HII galaxy Hubble diagram using Gaussian Processes, to confirm the validity of the CDD at a very high level of confidence. Using parameterizations η(z) = 1 + η 0 z and η(z) = 1 + η 1 z + η 2 z 2 , our best-fit results are η 0 = 0.0147 +0.056 −0.066 , and η 1 = 0.1091 +0.1680 −0.1568 and η 2 = −0.0603 +0.0999 −0.0988 , respectively. In spite of these strong constraints, however, we also point out that the analysis of strong lensing using a simplified single isothermal sphere (SIS) model for the lens produces some irreducible scatter in the inferred CDD data. The use of an extended SIS approximation, with a power-law density structure, yields very similar results, but does not lessen the scatter due to its larger number of free parameters, which weakens the best-fit constraints. Future work with these strong lenses should therefore be based on more detailed ray-tracing calculations to determine the mass distribution more precisely.

Revisiting the cosmic distance duality relation with machine learning reconstruction methods: the combination of HII galaxies and ultra-compact radio quasars

“…If η 3 increases to zero, then η 4 will go back to zero, which means that the strong degeneracy between them affects our test of CDDR validity. Such result, which is similar with the findings of previous works [11], highlights the importance of choosing a reliable parametrization to describe η(z) in the early universe. Benefit from the GP technology, the HII/QSO pairs satisfying the redshift selection criteria have a massive growth, therefore, a considerable amount of high-redshift samples (z > 1.4) have been included in our analysis.…”

“…From this figure, one can see that the 1σ uncertainty from GP reconstruction is smaller than that of individual data points. Such issue has been extensively discussed in the recent works [11,51]. More specifically, the final reconstructed confidence region depends on three factors, i.e., the observed errors of data, the optimization of hyper parameters of the GP method, and the product of the covariance matrixes K * K −1 y K T * between the predicted and current observed points.…”

“…Traditionally, testing CDDR needs two types of observational data sets, i.e., the luminosity distance derived from the luminous sources with known (or standardizable) intrinsic luminosity in the Universe like type-Ia supernova (SN Ia), and the angular diameter distance observed from Baryon Acoustic Oscillations (BAO) [6], Sunyaev-Zeldovich (SZ) effect in clusters with X-ray surface luminosity measurements [7][8][9], or strong gravitational lensing (SGL) [10,11], etc. However, it is necessary to point out that the luminosity distance inferred from SN Ia only covers the relatively lower redshift range z ≤ 1.4.…”

Probing the dark matter density evolution law with large scale structures

“…Usually, a lens could be a foreground galaxy or a cluster of galaxies positioned between a source (quasar) and an observer, where the multiple-image separation from the source only depends on the lens and source angular diameter distance (see, for instance, Refs. [31][32][33][34][35][36][37][38][39][40], where SGL systems were used recently as a cosmological tool). However, it is important to point out that the constraints obtained from SGL systems may depend on a model for the lens mass distribution (see next section).…”

Probing variation of the fine-structure constant in runaway dilaton models using Strong Gravitational Lensing and Type Ia Supernovae

“…For example, time-delay measurements of gravitational lensings can be used to measure the Hubble constant [56], and the cosmic diameter distance relation (CDDR) [57]. Other statistical properties of SGL can restrict the deceleration parameter of the universe [58], spacetime curvature [59,60], also departures of CDDR [61,62], cosmological constant [63], the speed of light [64], and others. It is a purely gravitational phenomenon occurring when the source (s), lens (l), and observer (o) are at the same signal line forming a structured ring called the Einstein radius (θ E ) [65].…”