Cosmological Model-independent Constraints on Spatial Curvature from Strong Gravitational Lensing and SN Ia Observations

In this paper, we perform a cosmological model-independent test of the cosmic distance–duality relation (CDDR) in terms of the ratio of angular diameter distance (ADD) [Formula: see text] from strong gravitational lensing (SGL) and the ratio of luminosity distance (LD) [Formula: see text] obtained from the joint of type Ia supernovae (SNIa) Union2.1 compilation and the latest Gamma-Ray Bursts (GRBs) data, where the superscripts s and l correspond to the redshifts [Formula: see text] and [Formula: see text] at the source and lens from SGL samples. The purpose of combining GRB data with SNIa compilation is to test CDDR in a wider redshift range. The LD associated with the redshifts of the observed ADD is obtained through two cosmological model-independent methods, namely, method A: binning the SNIa+GRBs data, and method B: reconstructing the function of DL by combining the Crossing Statistic with the smoothing method. We find that CDDR is compatible with the observations at [Formula: see text] confidence level for the power law model which is assumed to describe the mass distribution of lensing systems with method B in a wider redshift range.

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STRONG GRAVITATIONAL LENSING AND ITS COSMIC CONSTRAINTS

Modern Physics Letters A ◽

10.1142/s0217732313500570 ◽

2013 ◽

Vol 28 (14) ◽

pp. 1350057 ◽

Cited By ~ 7

Author(s):

NANNAN WANG ◽

LIXIN XU

Keyword(s):

Cosmological Model ◽

Gravitational Lensing ◽

Velocity Dispersion ◽

Model Space ◽

Data Sets ◽

Spatial Curvature ◽

Strong Gravitational Lensing ◽

Strong Lensing ◽

Λcdm Model ◽

Stellar Velocity

In this paper, we propose a new method to use the strong lensing data sets to constrain a cosmological model. By taking the ratio [Formula: see text] as cosmic observations, one can completely eliminate the uncertainty caused by the relation σSIS= fEσ0which characterizes the relation between the stellar velocity dispersion σ0and the velocity dispersion σSIS. Via our method, a relative tight constraint to the cosmological model space can be obtained, for the spatially flat ΛCDM model as an example [Formula: see text] in 3σ regions. And by using this method, one can also probe the nature of dark energy and the spatial curvature of our Universe.

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Test of the cosmic distance duality relation for arbitrary spatial curvature

Monthly Notices of the Royal Astronomical Society ◽

10.1093/mnras/stab124 ◽

2021 ◽

Vol 502 (3) ◽

pp. 3500-3509

Author(s):

Jin Qin ◽

Fulvio Melia ◽

Tong-Jie Zhang

Keyword(s):

Gravitational Lensing ◽

High Redshift ◽

Duality Relation ◽

Spatial Curvature ◽

Hubble Diagram ◽

Sis Model ◽

Strong Gravitational Lensing ◽

Best Fitting ◽

Model Independent ◽

The Universe

ABSTRACT The cosmic distance duality relation (CDDR), η(z) = (1 + z)2dA(z)/dL(z) = 1, is one of the most fundamental and crucial formulae in cosmology. This relation couples the luminosity and angular diameter distances, two of the most often used measures of structure in the Universe. We here propose a new model-independent method to test this relation, using strong gravitational lensing (SGL) and the high-redshift quasar Hubble diagram reconstructed with a Bézier parametric fit. We carry out this test without pre-assuming a zero spatial curvature, adopting instead the value ΩK = 0.001 ± 0.002 optimized by Planck in order to improve the reliability of our result. We parametrize the CDDR using η(z) = 1 + η0z, 1 + η1z + η2z2, and 1 + η3z/(1 + z), and consider both the SIS and non-SIS lens models for the strong lensing. Our best-fitting results are: $\eta _0=-0.021^{+0.068}_{-0.048}$, $\eta _1=-0.404^{+0.123}_{-0.090}$, $\eta _2=0.106^{+0.028}_{-0.034}$, and $\eta _3=-0.507^{+0.193}_{-0.133}$ for the SIS model, and $\eta _0=-0.109^{+0.044}_{-0.031}$ for the non-SIS model. The measured η(z), based on the Planck parameter ΩK, is essentially consistent with the value (=1) expected if the CDDR were fully respected. For the sake of comparison, we also carry out the test for other values of ΩK, but find that deviations of spatial flatness beyond the Planck optimization are in even greater tension with the CDDR. Future measurements of SGL may improve the statistics and alter this result but, as of now, we conclude that the CDDR favours a flat Universe.

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Model-independent Estimations for the Cosmic Curvature from the Latest Strong Gravitational Lensing Systems

The Astrophysical Journal ◽

10.3847/1538-4357/ab5f61 ◽

2020 ◽

Vol 889 (2) ◽

pp. 186 ◽

Cited By ~ 3

Author(s):

Huan Zhou ◽

Zhengxiang Li

Keyword(s):

Gravitational Lensing ◽

Strong Gravitational Lensing ◽

Model Independent

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Measurements of the Hubble constant and cosmic curvature with quasars: ultracompact radio structure and strong gravitational lensing

Monthly Notices of the Royal Astronomical Society ◽

10.1093/mnras/stab638 ◽

2021 ◽

Vol 503 (2) ◽

pp. 2179-2186

Author(s):

Jing-Zhao Qi ◽

Jia-Wei Zhao ◽

Shuo Cao ◽

Marek Biesiada ◽

Yuting Liu

Keyword(s):

Gravitational Lensing ◽

Cold Dark Matter ◽

Hubble Constant ◽

Spatial Curvature ◽

Radio Structure ◽

Strong Gravitational Lensing ◽

Flat Universe ◽

Long Baseline ◽

Local Distance ◽

The One

ABSTRACT Although the Hubble constant H0 and spatial curvature ΩK have been measured with very high precision, they still suffer from some tensions. In this paper, we propose an improved method to combine the observations of ultracompact structure in radio quasars and strong gravitational lensing with quasars acting as background sources to determine H0 and ΩK simultaneously. By applying the distance sum rule to the time-delay measurements of seven strong lensing systems and 120 intermediate-luminosity quasars calibrated as standard rulers, we obtain stringent constraints on the Hubble constant (H0 = 78.3 ± 2.9 km s−1 Mpc−1) and the cosmic curvature (ΩK = 0.49 ± 0.24). On the one hand, in the framework of a flat universe, the measured Hubble constant ($H_0=73.6^{+1.8}_{-1.6} \mathrm{\,km\,s^{-1}\,Mpc^{-1}}$) is strongly consistent with that derived from the local distance ladder, with a precision of 2 per cent. On the other hand, if we use the local H0 measurement as a prior, our results are marginally compatible with zero spatial curvature ($\Omega _K=0.23^{+0.15}_{-0.17}$) and there is no significant deviation from a flat universe. Finally, we also evaluate whether strongly lensed quasars would produce robust constraints on H0 and ΩK in the non-flat and flat Λ cold dark matter model, if the compact radio structure measurements are available from very long baseline interferometry observations.

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Generalized model-independent characterization of strong gravitational lenses V: reconstructing the lensing distance ratio by supernovae for a general Friedmann universe

Monthly Notices of the Royal Astronomical Society ◽

10.1093/mnras/stz2717 ◽

2019 ◽

Vol 490 (2) ◽

pp. 1913-1927

Author(s):

Jenny Wagner ◽

Sven Meyer

Keyword(s):

Time Delay ◽

Cosmological Model ◽

Gravitational Lensing ◽

Distance Measure ◽

Hubble Constant ◽

Distance Measures ◽

Gravitational Lenses ◽

Confidence Bounds ◽

Distance Ratio ◽

Model Independent

ABSTRACT We determine the cosmic expansion rate from supernovae of type Ia to set up a data-based distance measure that does not make assumptions about the constituents of the universe, i.e. about a specific parametrization of a Friedmann cosmological model. The scale, determined by the Hubble constant H0, is the only free cosmological parameter left in the gravitational lensing formalism. We investigate to which accuracy and precision the lensing distance ratio D is determined from the Pantheon sample. Inserting D and its uncertainty into the lensing equations for given H0, especially the time-delay equation between a pair of multiple images, allows to determine lens properties, especially differences in the lensing potential (Δϕ), without specifying a cosmological model. We expand the luminosity distances into an analytic orthonormal basis, determine the maximum-likelihood weights for the basis functions by a globally optimal χ2-parameter estimation, and derive confidence bounds by Monte Carlo simulations. For typical strong lensing configurations between z = 0.5 and 1.0, Δϕ can be determined with a relative imprecision of 1.7 per cent, assuming imprecisions of the time delay and the redshift of the lens on the order of 1 per cent. With only a small, tolerable loss in precision, the model-independent lens characterisation developed in this paper series can be generalised by dropping the specific Friedmann model to determine D in favour of a data-based distance ratio. Moreover, for any astrophysical application, the approach presented here, provides distance measures for z ≤ 2.3 that are valid in any homogeneous, isotropic universe with general relativity as theory of gravity.

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The first simultaneous measurement of Hubble constant and post-Newtonian parameter from time-delay strong lensing

Monthly Notices of the Royal Astronomical Society Letters ◽

10.1093/mnrasl/slaa107 ◽

2020 ◽

Vol 497 (1) ◽

pp. L56-L61 ◽

Cited By ~ 2

Author(s):

Tao Yang ◽

Simon Birrer ◽

Bin Hu

Keyword(s):

General Relativity ◽

Time Delay ◽

Cosmological Model ◽

Gravitational Lensing ◽

Hubble Constant ◽

Stellar Kinematics ◽

Local Universe ◽

Dynamical Mass ◽

Strong Gravitational Lensing ◽

Strong Lensing

ABSTRACT Strong gravitational lensing has been a powerful probe of cosmological models and gravity. To date, constraints in either domain have been obtained separately. We propose a new methodology through which the cosmological model, specifically the Hubble constant, and post-Newtonian parameter can be simultaneously constrained. Using the time-delay cosmography from strong lensing combined with the stellar kinematics of the deflector lens, we demonstrate that the Hubble constant and post-Newtonian parameter are incorporated in two distance ratios that reflect the lensing mass and dynamical mass, respectively. Through the re-analysis of the four publicly released lenses distance posteriors from the H0LiCOW (H0 Lenses in COSMOGRAIL’s Wellspring) collaboration, the simultaneous constraints of Hubble constant and post-Newtonian parameter are obtained. Our results suggest no deviation from the general relativity; $\gamma _{\tt {PPN}}=0.87^{+0.19}_{-0.17}$ with a Hubble constant that favours the local Universe value, $H_0=73.65^{+1.95}_{-2.26}$ km s−1 Mpc−1. Finally, we forecast the robustness of gravity tests by using the time-delay strong lensing for constraints we expect in the next few years. We find that the joint constraint from 40 lenses is able to reach the order of $7.7{{\ \rm per\ cent}}$ for the post-Newtonian parameter and $1.4{{\ \rm per\ cent}}$ for the Hubble constant.

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