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

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.

scholarly journals Generalised model-independent characterisation of strong gravitational lenses

2018 ◽  
Vol 620 ◽  
pp. A86 ◽  
Author(s):  
Jenny Wagner
Keyword(s):  
Time Delay ◽  
Gravitational Lensing ◽  
General Class ◽  
Deflection Angle ◽  
Lens Model ◽  
Gravitational Lenses ◽  
Source Position ◽  
Multiple Images ◽  
Model Independent ◽  
The Deflection Angle

Based on the standard gravitational lensing formalism with its effective, projected lensing potential in a given background cosmology, we investigated under which transformations of the source position and of the deflection angle the observable properties of the multiple images remain invariant. These observable properties are time delay differences, the relative image positions, relative shapes, and magnification ratios. As they only constrain local lens properties, we derive general, local invariance transformations in the areas covered by the multiple images. We show that the known global invariance transformations, for example, the mass-sheet transformation or the source position transformation, are contained in our invariance transformations, when they are restricted to the areas covered by the multiple images and when lens-model-based degeneracies are ignored, like the freedom to add or subtract masses in unconstrained regions without multiple images. Hence, we have identified the general class of invariance transformations that can occur, in particular in our model-independent local characterisation of strong gravitational lenses.

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

2020 ◽  
Vol 497 (1) ◽  
pp. L56-L61 ◽  
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.

scholarly journals Analysis of the Angular Dependence of Time Delay in Gravitational Lensing

2018 ◽  
Author(s):  
Nicola Alchera ◽  
Marco Bonici ◽  
Roberta Cardinale ◽  
Alba Domi ◽  
Nicola Maggiore ◽  
...  
Keyword(s):  
Time Delay ◽  
Angular Dependence ◽  
Gravitational Potential ◽  
Gravitational Lensing ◽  
Degrees Of Freedom ◽  
Hubble Constant ◽  
Smoothness Condition ◽  
Central Potential ◽  
Alternative Formula

We consider an alternative formula for time delay in gravitational lensing. Imposing a smoothness condition on the gravitationally deformed paths followed by the photons from the source to the observer, we show that our formula displays the same degrees of freedom of the standard one. In addition to this, it is shown that the standard expression for time delay is recovered when small angles are involved. These two features strongly support the claim that the formula for time delay studied in this paper is the generalization to arbitrary angles of the standard one, which is valid at small angles. This could therefore result in a useful tool in view of softening the known discrepancy between the various estimates of the Hubble constant. As an aside, two interesting consequences of our proposal for time delay are discussed: the existence of a constraint on the gravitational potential generated by the lens and a formula for the mass of the lens in the case of central potential.

scholarly journals TDCOSMO

2020 ◽  
Vol 642 ◽  
pp. A194 ◽  
Author(s):  
D. Gilman ◽  
S. Birrer ◽  
T. Treu
Keyword(s):  
Dark Matter ◽  
Time Delay ◽  
Time Delays ◽  
Arrival Time ◽  
Cosmological Parameters ◽  
Hubble Constant ◽  
Line Of Sight ◽  
Gravitational Lenses ◽  
Additional Source ◽  
Precision Limit

Time delay cosmography uses the arrival time delays between images in strong gravitational lenses to measure cosmological parameters, in particular the Hubble constant H0. The lens models used in time delay cosmography omit dark matter subhalos and line-of-sight halos because their effects are assumed to be negligible. We explicitly quantify this assumption by analyzing mock lens systems that include full populations of dark matter subhalos and line-of-sight halos, applying the same modeling assumptions used in the literature to infer H0. We base the mock lenses on six quadruply imaged quasars that have delivered measurements of the Hubble constant, and quantify the additional uncertainties and/or bias on a lens-by-lens basis. We show that omitting dark substructure does not bias inferences of H0. However, perturbations from substructure contribute an additional source of random uncertainty in the inferred value of H0 that scales as the square root of the lensing volume divided by the longest time delay. This additional source of uncertainty, for which we provide a fitting function, ranges from 0.7 − 2.4%. It may need to be incorporated in the error budget as the precision of cosmographic inferences from single lenses improves, and it sets a precision limit on inferences from single lenses.

scholarly journals HOLISMOKES

2020 ◽  
Vol 644 ◽  
pp. A162
Author(s):  
S. H. Suyu ◽  
S. Huber ◽  
R. Cañameras ◽  
M. Kromer ◽  
S. Schuldt ◽  
...  
Keyword(s):  
Time Delay ◽  
Gravitational Lensing ◽  
Early Phase ◽  
Rest Frame ◽  
Hubble Constant ◽  
Angular Diameter ◽  
Strong Gravitational Lensing ◽  
Space And Time ◽  
Precise Time

We present the HOLISMOKES programme on strong gravitational lensing of supernovae (SNe) as a probe of SN physics and cosmology. We investigate the effects of microlensing on early-phase SN Ia spectra using four different SN explosion models. We find that distortions of SN Ia spectra due to microlensing are typically negligible within ten rest-frame days after a SN explosion (< 1% distortion within the 1σ spread and ≲10% distortion within the 2σ spread). This shows the great prospects of using lensed SNe Ia to obtain intrinsic early-phase SN spectra for deciphering SN Ia progenitors. As a demonstration of the usefulness of lensed SNe Ia for cosmology, we simulate a sample of mock lensed SN Ia systems that are expected to have accurate and precise time-delay measurements in the era of the Rubin Observatory Legacy Survey of Space and Time (LSST). Adopting realistic yet conservative uncertainties on their time-delay distances and lens angular diameter distances, of 6.6% and 5%, respectively, we find that a sample of 20 lensed SNe Ia would allow us to constrain the Hubble constant (H0) with 1.3% uncertainty in the flat ΛCDM cosmology. We find a similar constraint on H0 in an open ΛCDM cosmology, while the constraint degrades to 3% in a flat wCDM cosmology. We anticipate lensed SNe to be an independent and powerful probe of SN physics and cosmology in the upcoming LSST era.

scholarly journals Generalised model-independent characterisation of strong gravitational lenses

2018 ◽  
Vol 615 ◽  
pp. A102 ◽  
Author(s):  
J. Wagner
Keyword(s):  
Gravitational Lensing ◽  
Taylor Expansion ◽  
Deflection Angle ◽  
Host Galaxy ◽  
Gravitational Lenses ◽  
Critical Curves ◽  
Independent Information ◽  
Model Independent ◽  
The Deflection Angle ◽  
Oriented Parallel

In galaxy-galaxy strong gravitational lensing, Einstein rings are generated when the lensing galaxy has an axisymmetric lensing potential and the source galaxy is aligned with its symmetry centre along the line of sight. Using a Taylor expansion around the Einstein radius and eliminating the unknown source, I derive a set of analytic equations that determine differences of the deflection angle of the perturber weighted by the convergence of the axisymmetric lens and ratios of the convergences at the positions of the arcs from the measurable thickness of the arcs. In the same manner, asymmetries in the brightness distributions along an arc determine differences in the deflection angle of the perturber if the source has a symmetric brightness profile and is oriented parallel to or orthogonal to the caustic. These equations are the only model-independent information retrievable from observations to leading order in the Taylor expansion. General constraints on the derivatives of the perturbing lens are derived such that the perturbation does not change the number of critical curves. To infer physical properties such as the mass of the perturber or its position, models need to be inserted. The same conclusions about the scale of detectable masses (of the order of 108M⊙) and model-dependent degeneracies as in other approaches are then found and supported by analysing B1938+666 as an example. Yet, the model-independent equations show that there is a fundamental degeneracy between the main lens and the perturber that can only be broken if their relative position is known. This explains the degeneracies between lens models already found in simulations from a more general viewpoint. Hence, apart from the radii and brightness distributions of the arcs, independent information on the axisymmetric lens or the perturber has to be employed to disentangle the axisymmetric lens and the perturber. Depending on the properties of the pertuber, this degeneracy can be broken by characterising the surrounding of the lens or by measuring the time delay between quasar images embedded in the perturbed Einstein ring of the host galaxy.

scholarly journals Testing the distance–duality relation from strong gravitational lensing, type Ia supernovae and gamma-ray bursts data up to redshift z ∼ 3.6

2017 ◽  
Vol 26 (09) ◽  
pp. 1750097 ◽  
Author(s):  
Xiangyun Fu ◽  
Pengcheng Li
Keyword(s):  
Cosmological Model ◽  
Gravitational Lensing ◽  
Gamma Ray ◽  
Gamma Ray Bursts ◽  
Type Ia Supernovae ◽  
Redshift Range ◽  
Strong Gravitational Lensing ◽  
Type Ia ◽  
Model Independent ◽  
Ia Supernovae

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.

scholarly journals A model-independent constraint on the Hubble constant with gravitational waves from the Einstein Telescope

2020 ◽  
Vol 29 (15) ◽  
pp. 2050105
Author(s):  
Sixuan Zhang ◽  
Shuo Cao ◽  
Jia Zhang ◽  
Tonghua Liu ◽  
Yuting Liu ◽  
...  
Keyword(s):  
Cosmological Model ◽  
Gravitational Wave ◽  
Gravitational Waves ◽  
Simulated Data ◽  
Hubble Constant ◽  
Host Galaxies ◽  
Local Universe ◽  
Binary Neutron Star ◽  
Einstein Telescope ◽  
Model Independent

In this paper, we investigate the expected constraints on the Hubble constant from the gravitational-wave standard sirens, in a cosmological-model-independent way. In the framework of the well-known Hubble law, the GW signal from each detected binary merger in the local universe ([Formula: see text]) provides a measurement of luminosity distance [Formula: see text] and thus the Hubble constant [Formula: see text]. Focusing on the simulated data of gravitational waves from the third-generation gravitational wave detector (the Einstein Telescope, ET), combined with the redshifts determined from electromagnetic counter parts and host galaxies, one can expect the Hubble constant to be constrained at the precision of [Formula: see text] with 20 well-observed binary neutron star (BNS) mergers. Additional standard-siren measurements from other types of future gravitational-wave sources (NS-BH and BBH) will provide more precision constraints of this important cosmological parameter. Therefore, we obtain that future measurements of the luminosity distances of gravitational waves sources will be much more competitive than the current analysis, which makes it expectable more vigorous and convincing constraints on the Hubble constant in a cosmological-model-independent way.

scholarly journals Accurate cosmology from gravitational-lens time delays

2012 ◽  
Vol 8 (S289) ◽  
pp. 331-338
Author(s):  
S. H. Suyu
Keyword(s):  
Time Delay ◽  
Time Delays ◽  
Cosmological Parameters ◽  
Hubble Constant ◽  
Gravitational Lens ◽  
Current Status ◽  
Gravitational Lenses ◽  
Distance Measurements ◽  
One Step

AbstractThe time delays between the multiple images of a strong gravitational-lens system, together with a model of the lens-mass distribution, provide a one-step determination of the time-delay distance, and thus a measure of cosmological parameters, particularly the Hubble constant, H0. I review the recent advances in measuring time-delay distances, and present the current status of cosmological constraints based on gravitational-lens time delays. In particular, I report the time-delay distance measurements of two gravitational lenses and their implication for cosmology from a recent study by Suyuet al.

scholarly journals H0LiCOW XII. Lens mass model of WFI2033 − 4723 and blind measurement of its time-delay distance and H0

2019 ◽  
Vol 498 (1) ◽  
pp. 1440-1468 ◽  
Author(s):  
Cristian E Rusu ◽  
Kenneth C Wong ◽  
Vivien Bonvin ◽  
Dominique Sluse ◽  
Sherry H Suyu ◽  
...  
Keyword(s):  
Time Delay ◽  
Hubble Space Telescope ◽  
Hubble Constant ◽  
Companion Paper ◽  
Wide Field ◽  
Full Time ◽  
Gravitational Lenses ◽  
Mass Model ◽  
Imaging And Spectroscopy ◽  
Field Imaging

ABSTRACT We present the lens mass model of the quadruply-imaged gravitationally lensed quasar WFI2033 − 4723, and perform a blind cosmographical analysis based on this system. Our analysis combines (1) time-delay measurements from 14 yr of data obtained by the COSmological MOnitoring of GRAvItational Lenses (COSMOGRAIL) collaboration, (2) high-resolution Hubble Space Telescope imaging, (3) a measurement of the velocity dispersion of the lens galaxy based on ESO-MUSE data, and (4) multi-band, wide-field imaging and spectroscopy characterizing the lens environment. We account for all known sources of systematics, including the influence of nearby perturbers and complex line-of-sight structure, as well as the parametrization of the light and mass profiles of the lensing galaxy. After unblinding, we determine the effective time-delay distance to be $4784_{-248}^{+399}~\mathrm{Mpc}$, an average precision of $6.6{{\ \rm per\ cent}}$. This translates to a Hubble constant $H_{0} = 71.6_{-4.9}^{+3.8}~\mathrm{km~s^{-1}~Mpc^{-1}}$, assuming a flat ΛCDM cosmology with a uniform prior on Ωm in the range [0.05, 0.5]. This work is part of the H0 Lenses in COSMOGRAIL’s Wellspring (H0LiCOW) collaboration, and the full time-delay cosmography results from a total of six strongly lensed systems are presented in a companion paper (H0LiCOW XIII).

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