REVISITING STUDIES OF THE STATISTICAL PROPERTY OF A STRONG GRAVITATIONAL LENS SYSTEM AND MODEL-INDEPENDENT CONSTRAINT ON THE CURVATURE OF THE UNIVERSE

The language of ∞-categories provides an insightful new way of expressing many results in higher-dimensional mathematics but can be challenging for the uninitiated. To explain what exactly an ∞-category is requires various technical models, raising the question of how they might be compared. To overcome this, a model-independent approach is desired, so that theorems proven with any model would apply to them all. This text develops the theory of ∞-categories from first principles in a model-independent fashion using the axiomatic framework of an ∞-cosmos, the universe in which ∞-categories live as objects. An ∞-cosmos is a fertile setting for the formal category theory of ∞-categories, and in this way the foundational proofs in ∞-category theory closely resemble the classical foundations of ordinary category theory. Equipped with exercises and appendices with background material, this first introduction is meant for students and researchers who have a strong foundation in classical 1-category theory.

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Can We Measure H0 with VLBI Observations of Gravitational Images?

Symposium - International Astronomical Union ◽

10.1017/s0074180900134485 ◽

1988 ◽

Vol 129 ◽

pp. 207-208

Author(s):

E. E. Falco ◽

M. V. Gorenstein ◽

I. I. Shapiro

Keyword(s):

Time Delay ◽

Mass Distribution ◽

Velocity Dispersion ◽

Gravitational Lens ◽

Lens System ◽

Relative Time ◽

Surface Mass ◽

A Value ◽

Vlbi Observations ◽

The Difference

We have used the relative positions and magnifications of the A and B images in the gravitational lens system 0957+561, obtained from VLBI observations, to constrain a model for the surface mass distribution of the lens. With measurements of the difference ΔτBA in propagation times associated with A and B (the “relative time delay”) and of the velocity dispersion of the main lensing galaxy, both to be obtained, our model will yield a value for H0 with an uncertainty of ∼ 20% due mainly to uncertainties in our assumptions.

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Model-independent cosmic acceleration and redshift-dependent intrinsic luminosity in type-Ia supernovae

Astronomy and Astrophysics ◽

10.1051/0004-6361/201833032 ◽

2019 ◽

Vol 625 ◽

pp. A15 ◽

Cited By ~ 8

Author(s):

I. Tutusaus ◽

B. Lamine ◽

A. Blanchard

Keyword(s):

Spline Interpolation ◽

High Redshift ◽

Cosmic Acceleration ◽

Expansion Rate ◽

Type Ia Supernovae ◽

Type Ia ◽

Model Independent ◽

Ia Supernovae ◽

The Universe ◽

Intrinsic Luminosity

Context. The cosmological concordance model (ΛCDM) is the current standard model in cosmology thanks to its ability to reproduce the observations. The first observational evidence for this model appeared roughly 20 years ago from the type-Ia supernovae (SNIa) Hubble diagram from two different groups. However, there has been some debate in the literature concerning the statistical treatment of SNIa, and their stature as proof of cosmic acceleration. Aims. In this paper we relax the standard assumption that SNIa intrinsic luminosity is independent of redshift, and examine whether it may have an impact on our cosmological knowledge and more precisely on the accelerated nature of the expansion of the universe. Methods. To maximise the scope of this study, we do not specify a given cosmological model, but we reconstruct the expansion rate of the universe through a cubic spline interpolation fitting the observations of the different cosmological probes: SNIa, baryon acoustic oscillations (BAO), and the high-redshift information from the cosmic microwave background (CMB). Results. We show that when SNIa intrinsic luminosity is not allowed to vary as a function of redshift, cosmic acceleration is definitely proven in a model-independent approach. However, allowing for redshift dependence, a nonaccelerated reconstruction of the expansion rate is able to fit, at the same level of ΛCDM, the combination of SNIa and BAO data, both treating the BAO standard ruler rd as a free parameter (not entering on the physics governing the BAO), and adding the recently published prior from CMB observations. We further extend the analysis by including the CMB data. In this case we also consider a third way to combine the different probes by explicitly computing rd from the physics of the early universe, and we show that a nonaccelerated reconstruction is able to nicely fit this combination of low- and high-redshift data. We also check that this reconstruction is compatible with the latest measurements of the growth rate of matter perturbations. We finally show that the value of the Hubble constant (H0) predicted by this reconstruction is in tension with model-independent measurements. Conclusions. We present a model-independent reconstruction of a nonaccelerated expansion rate of the universe that is able to fit all the main background cosmological probes nicely. However, the predicted value of H0 is in tension with recent direct measurements. Our analysis points out that a final reliable and consensual value for H0 is critical to definitively prove cosmic acceleration in a model-independent way.

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Inner dark matter distribution of the Cosmic Horseshoe (J1148+1930) with gravitational lensing and dynamics

Astronomy and Astrophysics ◽

10.1051/0004-6361/201935042 ◽

2019 ◽

Vol 631 ◽

pp. A40 ◽

Cited By ~ 4

Author(s):

S. Schuldt ◽

G. Chirivì ◽

S. H. Suyu ◽

A. Yıldırım ◽

A. Sonnenfeld ◽

...

Keyword(s):

Dark Matter ◽

Gravitational Lensing ◽

Gravitational Lens ◽

Wide Field ◽

Lens System ◽

Matter Distribution ◽

Mass Model ◽

Luminous Matter ◽

Dark Matter Distribution ◽

Light Components

We present a detailed analysis of the inner mass structure of the Cosmic Horseshoe (J1148+1930) strong gravitational lens system observed with the Hubble Space Telescope (HST) Wide Field Camera 3 (WFC3). In addition to the spectacular Einstein ring, this systems shows a radial arc. We obtained the redshift of the radial arc counterimage zs, r = 1.961 ± 0.001 from Gemini observations. To disentangle the dark and luminous matter, we considered three different profiles for the dark matter (DM) distribution: a power law profile, the Navarro, Frenk, and White (NFW) profile, and a generalized version of the NFW profile. For the luminous matter distribution, we based the model on the observed light distribution that is fitted with three components: a point mass for the central light component resembling an active galactic nucleus, and the remaining two extended light components scaled by a constant mass-to-light ratio (M/L). To constrain the model further, we included published velocity dispersion measurements of the lens galaxy and performed a self-consistent lensing and axisymmetric Jeans dynamical modeling. Our model fits well to the observations including the radial arc, independent of the DM profile. Depending on the DM profile, we get a DM fraction between 60% and 70%. With our composite mass model we find that the radial arc helps to constrain the inner DM distribution of the Cosmic Horseshoe independently of the DM profile.

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Gravitational Lens System PS J0147+4630 (Andromeda’s Parachute): Main Lensing Galaxy and Optical Variability of the Quasar Images

The Astrophysical Journal ◽

10.3847/1538-4357/ab5063 ◽

2019 ◽

Vol 887 (2) ◽

pp. 126

Author(s):

Luis J. Goicoechea ◽

Vyacheslav N. Shalyapin

Keyword(s):

Gravitational Lens ◽

Optical Variability ◽

Lens System

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Search for Radio Recombination Lines towards the Gravitational Lens PKS1830-211

Symposium - International Astronomical Union ◽

10.1017/s0074180900168676 ◽

2002 ◽

Vol 199 ◽

pp. 116-117

Author(s):

N.R. Mohan ◽

K.R. Anantharamaiah ◽

W.M. Goss

Keyword(s):

Flux Density ◽

Emission Measure ◽

Gravitational Lens ◽

Lens System ◽

Frequency Range ◽

Ionized Gas ◽

Density Measurements ◽

Radio Recombination Lines ◽

Upper Limits ◽

Single Epoch

A search for radio recombination lines near 20 cm at z=0.193 and z=0.886 towards the gravitational lens system PKS1830-211 has yielded upper limits of |τL| ≤ 5 × 10−5 and ≤ 5 × 10−4 at the two redshifts respectively. Based on the non-detections, we derive upper limits to the emission measure of the ionized gas in the absorbing systems. We also present continuum flux density measurements over the frequency range 0.3—45 GHz made at a single epoch.

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Gaia GraL: Gaia DR2 gravitational lens systems

Astronomy and Astrophysics ◽

10.1051/0004-6361/201833480 ◽

2018 ◽

Vol 618 ◽

pp. A56 ◽

Cited By ~ 7

Author(s):

C. Ducourant ◽

O. Wertz ◽

A. Krone-Martins ◽

R. Teixeira ◽

J.-F. Le Campion ◽

...

Keyword(s):

Spatial Resolution ◽

Space Mission ◽

Gravitational Lens ◽

Model Parameters ◽

Gravitational Lenses ◽

Bayesian Modelling ◽

Lens System ◽

Data Release ◽

Gaia Dr2 ◽

Exhaustive List

Context. Thanks to its spatial resolution, the ESA/Gaia space mission offers a unique opportunity to discover new multiply imaged quasars and to study the already known lensed systems at sub-milliarcsecond astrometric precisions. Aims. In this paper, we address the detection of the known multiply imaged quasars from the Gaia Data Release 2 (DR2) and determine the astrometric and photometric properties of the individually detected images found in the Gaia DR2 catalogue. Methods. We have compiled an exhaustive list of quasar gravitational lenses from the literature to search for counterparts in the Gaia DR2. We then analysed the astrometric and photometric properties of these Gaia’s detections. To highlight the tremendous potential of Gaia at the sub-milliarcsecond level we finally performed a simple Bayesian modelling of the well-known gravitational lens system HE0435-1223, using Gaia DR2 and HST astrometry. Results. From 481 known multiply imaged quasars, 206 have at least one image found in the Gaia DR2. Among the 44 known quadruply imaged quasars of the list, 29 have at least one image in the Gaia DR2, 12 of which are fully detected (2MASX J01471020+4630433, HE 0435-1223, SDSS1004+4112, PG1115+080, RXJ1131-1231, 2MASS J11344050-2103230, 2MASS J13102005-1714579, B1422+231, J1606-2333, J1721+8842, WFI2033-4723, WGD2038-4008), eight have three counterparts, eight have two and one has only one. As expected, the modelling of HE0435-1223 shows that the model parameters are significantly better constrained when using Gaia astrometry compared to HST astrometry, in particular the relative positions of the background quasar source and the centroid of the deflector. The Gaia sub-milliarcsecond astrometry also significantly reduces the parameter correlations. Conclusions. Besides providing an up-to-date list of multiply imaged quasars and their detection in the Gaia DR2, this paper shows that more complex modelling scenarios will certainly benefit from Gaia sub-milliarcsecond astrometry.

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A large arc in the gravitational lens system 0957 + 561

The Astronomical Journal ◽

10.1086/116474 ◽

1993 ◽

Vol 105 ◽

pp. 816 ◽

Cited By ~ 23

Author(s):

G. M. Bernstein ◽

J. A. Tyson ◽

C. S. Kochanek

Keyword(s):

Gravitational Lens ◽

Lens System

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