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The recent Planck Legacy 2018 release has confirmed the presence of an enhanced lensing amplitude in CMB power spectra compared to that predicted in the standard $\Lambda$CDM model. A closed universe can provide a physical explanation for…

Cosmology and Nongalactic Astrophysics · Physics 2019-11-07 Eleonora Di Valentino , Alessandro Melchiorri , Joseph Silk

In the standard flat cosmological constant ($\Lambda$) cold dark matter (CDM) cosmology, a model of two populations of lens halos for strong gravitational lensing can reproduce the results of the Jodrell-Bank VLA Astrometric Survey (JVAS)…

Astrophysics · Physics 2009-11-10 Da-Ming Chen

We present Hubble Space Telescope images and 2 years of optical photometry of the quadruple quasar HE0435-1223. The time delays between the intrinsic quasar variations are 14.4+/-0.8 (A-D), 8.0+/-0.8 (A-B) and 2.1+/-0.8 (A-C) days. We also…

Astrophysics · Physics 2008-11-26 C. S. Kochanek , N. D. Morgan , E. E. Falco , B. A. McLeod , J. N. Winn , J. Dembicky , B. Ketzeback

The observed discrepancy of the Hubble parameter measurements in the local universe with the cosmic microwave background (CMB) data may indicate a new physics. It is vital to test the alternative models that reconcile the Hubble tension…

Cosmology and Nongalactic Astrophysics · Physics 2021-09-03 Hossein Moshafi , Shant Baghram , Nima Khosravi

Gravitational lensing provides a strict test of cosmogonic models. Detailed numerical propagation of light rays through a universe having a distribution of inhomogeneities derived from the standard CDM (cold dark matter) scenario with the…

Astrophysics · Physics 2010-12-13 Joachim Wambsganss , Renyue Cen , Jeremiah P. Ostriker , Edwin L. Turner

Strong gravitational lensing by galaxies is a powerful tool for studying cosmology and galaxy structure. The China Space Station Telescope (CSST) will revolutionize this field by discovering up to $\sim$100,000 galaxy-scale strong lenses, a…

Cosmology and Nongalactic Astrophysics · Physics 2025-11-12 Hengyu Wu , Yun Chen , Tonghua Liu , Xiaoyue Cao , Tian Li , Hui Li , Nan Li , Ran Li , Tengpeng Xu

In recent years, breakthroughs in methods and data have enabled gravitational time delays to emerge as a very powerful tool to measure the Hubble constant $H_0$. However, published state-of-the-art analyses require of order 1 year of expert…

Strongly gravitational lensed quasars can be used to measure the so-called time-delay distance $D_{\Delta t}$, and thus the Hubble constant $H_0$ and other cosmological parameters. Stellar kinematics of the deflector galaxy play an…

Cosmology and Nongalactic Astrophysics · Physics 2018-04-17 Anowar J. Shajib , Tommaso Treu , Adriano Agnello

In this paper we investigate the statistical properties of gravitational lenses for models in which a cosmological term decreases with time as $\Lambda \propto a^{-m}$, where $a$ is the scale factor and $m$ is a parameter ($0 \leq m < 3$).…

Astrophysics · Physics 2015-06-24 L. F. Bloomfield Torres , I. Waga

Observed time delays between images of a lensed QSO lead to the determination of the Hubble constant by Refsdal's method, provided the mass distribution in the lensing galaxy is reasonably well known. Since the two or four QSO images…

Astrophysics · Physics 2009-10-31 Liliya L. R. Williams , Prasenjit Saha

Galaxies located in the environment or on the line of sight towards gravitational lenses can significantly affect lensing observables, and can lead to systematic errors on the measurement of $H_0$ from the time-delay technique. We present…

Gravitational lensing and stellar dynamics provide two complementary, nearly orthogonal, constraints on the mass distribution of early-type lens galaxies. This allows the luminous and dark-matter distribution in higher-redshift (z>0.1)…

Astrophysics · Physics 2007-05-23 L. V. E. Koopmans

We present a blind time-delay cosmographic analysis for the lens system DES J0408$-$5354. This system is extraordinary for the presence of two sets of multiple images at different redshifts, which provide the opportunity to obtain more…

In standard CDM halo models, the time delay of a gravitational lens is determined by the cold baryon mass fraction, f, of the visible galaxy relative to the overall halo. The observed time delays in PG1115+080, SBS1520+530, B1600+434 and…

Astrophysics · Physics 2009-11-07 C. S. Kochanek

The current cosmological probes have provided a fantastic confirmation of the standard $\Lambda$ Cold Dark Matter cosmological model, that has been constrained with unprecedented accuracy. However, with the increase of the experimental…

Cosmology and Nongalactic Astrophysics · Physics 2021-05-27 Eleonora Di Valentino , Luis A. Anchordoqui , Ozgur Akarsu , Yacine Ali-Haimoud , Luca Amendola , Nikki Arendse , Marika Asgari , Mario Ballardini , Spyros Basilakos , Elia Battistelli , Micol Benetti , Simon Birrer , François R. Bouchet , Marco Bruni , Erminia Calabrese , David Camarena , Salvatore Capozziello , Angela Chen , Jens Chluba , Anton Chudaykin , Eoin Ó Colgáin , Francis-Yan Cyr-Racine , Paolo de Bernardis , Javier de Cruz Pérez , Jacques Delabrouille , Jo Dunkley , Celia Escamilla-Rivera , Agnès Ferté , Fabio Finelli , Wendy Freedman , Noemi Frusciante , Elena Giusarma , Adrià Gómez-Valent , Julien Guy , Will Handley , Ian Harrison , Luke Hart , Alan Heavens , Hendrik Hildebrandt , Daniel Holz , Dragan Huterer , Mikhail M. Ivanov , Shahab Joudaki , Marc Kamionkowski , Tanvi Karwal , Lloyd Knox , Suresh Kumar , Luca Lamagna , Julien Lesgourgues , Matteo Lucca , Valerio Marra , Silvia Masi , Sabino Matarrese , Arindam Mazumdar , Alessandro Melchiorri , Olga Mena , Laura Mersini-Houghton , Vivian Miranda , Cristian Moreno-Pulido , David F. Mota , Jessica Muir , Ankan Mukherjee , Florian Niedermann , Alessio Notari , Rafael C. Nunes , Francesco Pace , Andronikos Paliathanasis , Antonella Palmese , Supriya Pan , Daniela Paoletti , Valeria Pettorino , Francesco Piacentini , Vivian Poulin , Marco Raveri , Adam G. Riess , Vincenzo Salzano , Emmanuel N. Saridakis , Anjan A. Sen , Arman Shafieloo , Anowar J. Shajib , Joseph Silk , Alessandra Silvestri , Martin S. Sloth , Tristan L. Smith , Joan Solà , Carsten van de Bruck , Licia Verde , Luca Visinelli , Benjamin D. Wandelt , Deng Wang , Jian-Min Wang , Anil K. Yadav , Weiqiang Yang

Strong gravitational lensing provides a geometric probe of cosmology in a unique manner through distance ratios involving the source and lens. This is well known for the time delay distance derived from measured delays between lightcurves…

Cosmology and Nongalactic Astrophysics · Physics 2016-10-12 Eric V. Linder

The standard $\Lambda$ Cold Dark Matter cosmological model provides an amazing description of a wide range of astrophysical and astronomical data. However, there are a few big open questions, that make the standard model look like a…

Cosmology and Nongalactic Astrophysics · Physics 2021-05-27 Eleonora Di Valentino , Luis A. Anchordoqui , Ozgur Akarsu , Yacine Ali-Haimoud , Luca Amendola , Nikki Arendse , Marika Asgari , Mario Ballardini , Spyros Basilakos , Elia Battistelli , Micol Benetti , Simon Birrer , François R. Bouchet , Marco Bruni , Erminia Calabrese , David Camarena , Salvatore Capozziello , Angela Chen , Jens Chluba , Anton Chudaykin , Eoin Ó Colgáin , Francis-Yan Cyr-Racine , Paolo de Bernardis , Javier de Cruz Pérez , Jacques Delabrouille , Jo Dunkley , Celia Escamilla-Rivera , Agnès Ferté , Fabio Finelli , Wendy Freedman , Noemi Frusciante , Elena Giusarma , Adrià Gómez-Valent , Will Handley , Ian Harrison , Luke Hart , Alan Heavens , Hendrik Hildebrandt , Daniel Holz , Dragan Huterer , Mikhail M. Ivanov , Shahab Joudaki , Marc Kamionkowski , Tanvi Karwal , Lloyd Knox , Suresh Kumar , Luca Lamagna , Julien Lesgourgues , Matteo Lucca , Valerio Marra , Silvia Masi , Sabino Matarrese , Arindam Mazumdar , Alessandro Melchiorri , Olga Mena , Laura Mersini-Houghton , Vivian Miranda , Cristian Moreno-Pulido , David F. Mota , Jessica Muir , Ankan Mukherjee , Florian Niedermann , Alessio Notari , Rafael C. Nunes , Francesco Pace , Andronikos Paliathanasis , Antonella Palmese , Supriya Pan , Daniela Paoletti , Valeria Pettorino , Francesco Piacentini , Vivian Poulin , Marco Raveri , Adam G. Riess , Vincenzo Salzano , Emmanuel N. Saridakis , Anjan A. Sen , Arman Shafieloo , Anowar J. Shajib , Joseph Silk , Alessandra Silvestri , Martin S. Sloth , Tristan L. Smith , Joan Solà , Carsten van de Bruck , Licia Verde , Luca Visinelli , Benjamin D. Wandelt , Deng Wang , Jian-Min Wang , Anil K. Yadav , Weiqiang Yang

In these lectures I give an overview of gravitational lensing, concentrating on theoretical aspects, including derivations of some of the important results. Topics covered include the determination of surface mass densities of intervening…

Cosmology and Nongalactic Astrophysics · Physics 2017-03-08 Alan Heavens

One challenge in strong gravitational lensing cosmography is the measurement of time delays between multiple lensed images, which are essential for constraining the Hubble constant (\(H_0\)). In this study, we investigate how assumptions…

Cosmology and Nongalactic Astrophysics · Physics 2026-05-20 Guanhua Rui , Bin Hu , Wei Du

We develop the spacetime approach to gravitational lensing by spherically symmetric perturbations of flat, cosmological constant-dominated Friedman-Robertson-Walker metrics. The geodesics of the spacetime are expressed as integral…

General Relativity and Quantum Cosmology · Physics 2025-08-19 Thomas P. Kling , Sophia MacQueen Pooler
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