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Time delays from strong gravitational lensing provide a one-step absolute distance measurement. Thus, they measure $H_0$ independently of all other probes. We first review the foundations and history of time-delay cosmography. Then, we illustrate the current state of the art by means of two recent case studies that have been real breakthroughs: i) the quadruply imaged quasar lensed by a galaxy-scale deflector RXJ1131$-$1231, for which spatially resolved stellar kinematics is available; ii) the multiply imaged supernova "Refsdal", the first with measured time delays, lensed by cluster MACS1149.5$+$2223. We conclude by discussing the exciting future prospects of time-delay cosmography in the coming decade., Invited chapter for the edited book "Hubble Constant Tension" (Eds. E. Di Valentino and D. Brout, Springer Singapore, expected in 2024)

Context. Strong lenses are a biased subset of the general population of galaxies. Aims. The goal of this work is to quantify how lens galaxies and lensed sources differ from their parent distribution, namely the strong lensing bias. Methods. We first studied how the strong lensing cross-section varies as a function of lens and source properties. Then, we simulated strong lensing surveys with data similar to that expected for Euclid and measured the strong lensing bias in different scenarios. We focused particularly on two quantities: the stellar population synthesis mismatch parameter, $\alpha_{sps}$, defined as the ratio between the true stellar mass of a galaxy and the stellar mass obtained from photometry, and the central dark matter mass at fixed stellar mass and size. Results. Strong lens galaxies are biased towards larger stellar masses, smaller half-mass radii and larger dark matter masses. The amplitude of the bias depends on the intrinsic scatter in the mass-related parameters of the galaxy population and on the completeness in Einstein radius of the lens sample. For values of the scatter that are consistent with observed scaling relations and a minimum detectable Einstein radius of $0.5''$, the strong lensing bias in $\alpha_{sps}$ is $10\%$, while that in the central dark matter mass is $5\%$. The bias has little dependence on the properties of the source population: samples of galaxy-galaxy lenses and galaxy-quasar lenses that probe the same Einstein radius distribution are biased in a very similar way. Quadruply imaged quasar lenses, however, are biased towards higher ellipticity galaxies. Conclusions. Given current uncertainties, strong lensing observations can be used directly to improve our current knowledge of the inner structure of galaxies, without the need to correct for selection effects., Comment: Submitted to Astronomy & Astrophysics. A two-minute summary video of this paper is available at https://youtu.be/UmS9jRHTmZU

Multiply lensed sources experience a relative time delay in the arrival of photons. This effect can be used to measure absolute distances and the Hubble constant ($H_0$) and is known as time-delay cosmography. The methodology is independent of the local distance ladder and early-universe physics and provides a precise and competitive measurement of $H_0$. With upcoming observatories, time-delay cosmography can provide a 1% precision measurement of $H_0$ and can decisively shed light on the current reported 'Hubble tension'. This paper presents the theoretical background and the current techniques applied for time-delay cosmographic studies and the measurement of the Hubble constant. The paper describes the challenges and systematics in the different components of the analysis and strategies to mitigate them. The current measurements are discussed in context and the opportunities with the anticipated data sets in the future are laid out., 26 pages, 11 figures, to be submitted to Space Science Reviews, Topical Collection 'Strong Gravitational Lensing', eds. J. Wambsganss et al, added references with minor changes

Imaging data is the principal observable required to use galaxy-scale strong lensing in a multitude of applications in extragalactic astrophysics and cosmology. In this paper, we develop Lensing Exposure Time Calculator (LensingETC) to optimize the efficiency of telescope time usage when planning multi-filter imaging campaigns for galaxy-scale strong lenses. This tool simulates realistic data tailored to specified instrument characteristics and then automatically models them to assess the power of the data in constraining lens model parameters. We demonstrate a use case of this tool by optimizing a two-filter observing strategy (in IR and UVIS) within the limited exposure time per system allowed by a Hubble Space Telescope (HST) Snapshot program. We find that higher resolution is more advantageous to gain constraining power on the lensing observables, when there is a trade-off between signal-to-noise ratio and resolution; e.g., between the UVIS and IR filters of the HST. We also find that, whereas a point spread function (PSF) with sub-Nyquist sampling allows the sample mean for a model parameter to be robustly recovered for both galaxy-galaxy and point-source lensing systems, a sub-Nyquist sampled PSF introduces a larger scatter than a Nyquist sampled one in the deviation from the ground truth for point-source lens systems., 10 pages, 7 figures, 3 tables

To use strong gravitational lenses as an astrophysical or cosmological probe, models of their mass distributions are often needed. We present a new, time-efficient automation code for uniform modeling of strongly lensed quasars with GLEE, a lens modeling software, for high-resolution multi-band data. By using the observed positions of the lensed quasars and the spatially extended surface brightness distribution of the lensed quasar host galaxy, we obtain a model of the mass distribution of the lens galaxy. We apply this uniform modeling pipeline to a sample of nine strongly lensed quasars with HST WFC 3 images. The models show in most cases well reconstructed light components and a good alignment between mass and light centroids. We find that the automated modeling code significantly reduces the user input time during the modeling process. The preparation time of required input files is reduced significantly. This automated modeling pipeline can efficiently produce uniform models of extensive lens system samples which can be used for further cosmological analysis. A blind test through a comparison with the results of an independent automated modeling pipeline based on the modeling software Lenstronomy reveals important lessons. Quantities such as Einstein radius, astrometry, mass flattening and position angle are generally robustly determined. Other quantities depend crucially on the quality of the data and the accuracy of the PSF reconstruction. Better data and/or more detailed analysis will be necessary to elevate our automated models to cosmography grade. Nevertheless, our pipeline enables the quick selection of lenses for follow-up monitoring and further modeling, significantly speeding up the construction of cosmography-grade models. This is an important step forward to take advantage of the orders of magnitude increase in the number of lenses expected in the coming decade., Comment: 37 pages, 14 figures, published in A&A

Strong lensing at the galaxy scale is useful for numerous applications in Astrophysics and Cosmology. Some of the principal applications are studying the mass structure, formation, and evolution of elliptical galaxies, constraining the stellar initial mass function, and measuring cosmological parameters. Since the first discovery of a galaxy-scale strong lens in the eighties, this field has come a long way regarding data quality and techniques to model the data. In this review article, we describe the most common methodologies to model lensing observables of galaxy-scale strong lenses, especially the imaging data, as it is the most available and informative source of lensing observables. We review the main results from the literature in astrophysical and cosmological applications of galaxy-scale strong lenses. We also discuss the current limitations of the data and methodologies and provide a future outlook of the expected development and improvements in both aspects in the near future., Comment: To be submitted to Space Science Reviews, Topical Collection "Strong Gravitational Lensing", eds. J. Wambsganss et al. This version: updated references

We have measured the redshifts and single-aperture velocity dispersions of eight lens galaxies using the data collected by the Echellette Spectrograph and Imager (ESI) and Low Resolution Imaging Spectrometer (LRIS) at W.M. Keck observatory on different observing nights spread over three years (2018-2020). These results, combined with other ancillary data, such as high-resolution images of the lens systems, and time delays, are necessary to increase the sample size of the quasar-galaxy lens systems for which the Hubble constant can be measured, using the time-delay strong lensing method, hence increasing the precision of its inference. Typically, the 2D spectra of the quasar-galaxy lens systems get spatially blended due to seeing by ground-based observations. As a result, the extracted lensing galaxy (deflector) spectra become significantly contaminated by quasar light, which affects the ability to extract meaningful information about the deflector. To account for spatial blending and extract less contaminated and higher signal-to-noise ratio (S/N) 1D spectra of the deflectors, a forward modeling method has been implemented. From the extracted spectra, we have measured redshifts using prominent absorption lines and single aperture velocity dispersions using the penalized pixel fitting code pPXF. In this paper, we report the redshifts and single aperture velocity dispersions of eight lens galaxies - J0147+4630, B0445+123, B0631+519, J0659+1629, J0818-2613, J0924+0219, J1433+6007, and J1817+2729. Among these systems, six do not have previously measured velocity dispersions; for the other two, our measurements are consistent with previously reported values. Additionally, we have measured the previously unknown redshifts of the deflectors in J0818-2613 and J1817+2729 to be $0.866 \pm 0.002$ and $0.408 \pm 0.002$, respectively., Comment: 13 pages, 6 figures, 3 tables; accepted in A&A

We perform a search for galaxy-galaxy strong lens systems using a convolutional neural network (CNN) applied to imaging data from the first public data release of the DECam Local Volume Exploration Survey (DELVE), which contains $\sim 520$ million astronomical sources covering $\sim 4,000$ $\mathrm{deg}^2$ of the southern sky to a $5σ$ point-source depth of $g=24.3$, $r=23.9$, $i=23.3$, and $z=22.8$ mag. Following the methodology of similar searches using DECam data, we apply color and magnitude cuts to select a catalog of $\sim 11$ million extended astronomical sources. After scoring with our CNN, the highest scoring 50,000 images were visually inspected and assigned a score on a scale from 0 (definitely not a lens) to 3 (very probable lens). We present a list of 617 strong lens candidates, 599 of which are previously unreported. We categorize our candidates using their human-assigned scores, resulting in 60 Grade A candidates, 160 Grade B candidates, and 397 Grade C candidates. We additionally highlight 8 potential quadruply lensed quasars from this sample. Due to the location of our search footprint in the northern Galactic cap ($b > 10$ deg) and southern celestial hemisphere (${\rm Dec.}, 27 pages; added machine-readable table

The standard Λ Cold Dark Matter cosmological model provides a wonderful fit to current cosmological data, but a few statistically significant tensions and anomalies were found in the latest data analyses. While these anomalies could be due to the presence of systematic errors in the experiments, they could also indicate the need for new physics beyond the standard model. In this Letter of Interest we focus on the tension between Planck data and weak lensing measurements and redshift surveys, in the value of the matter energy density Ωm and the amplitude σ8 (or the growth rate fσ8) of cosmic structure. We list a few promising models for solving this tension, and discuss the importance of trying to fit multiple cosmological datasets with complete physical models, rather than fitting individual datasets with a few handpicked theoretical parameters.

The standard $\Lambda$ Cold Dark Matter cosmological model provides a wonderful fit to current cosmological data, but a few tensions and anomalies became statistically significant with the latest data analyses. While these anomalies could be due to the presence of systematic errors in the experiments, they could also indicate the need for new physics beyond the standard model. In this Letter of Interest we focus on the tension of the Planck data with weak lensing measurements and redshift surveys, about the value of the matter energy density $\Omega_m$, and the amplitude or rate of the growth of structure ($\sigma_8,f\sigma_8$). We list a few interesting models for solving this tension, and we discuss the importance of trying to fit with a single model a full array of data and not just one parameter at a time., Comment: Snowmass2021 - Letter of Interest

Strong gravitational lens systems with time delays between the multiple images are a powerful probe of cosmology, particularly of the Hubble constant (H0). The H0 Lenses In COSMOGRAIL's Wellspring (H0LiCOW) project has measured H0 from lensed quasars using deep Hubble Space Telescope and AO imaging, precise time delay measurements from the COSMOGRAIL monitoring project, a measurement of the velocity dispersion of the lens galaxies, and a characterization of the mass distribution along the line of sight. Our latest results from a total of six lenses constrains H0 to be 73.3(-1.8,+1.7) km/s/Mpc for a flat Lambda CDM cosmology, which is a measurement to 2.4% precision. These results are consistent with independent determinations of H0 using type Ia supernovae calibrated by the distance ladder method, and are in 3.1-sigma tension with the results of Planck CMB measurements. Combined with the latest distance ladder results from the SH0ES project, we find a 5.3-sigma tension between Planck and late-Universe probes, hinting at possible new physics beyond the standard LCDM model and highlighting the importance of this independent probe.

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 sensitivity a few statistically significant tensions between different independent cosmological datasets emerged. While these tensions can be in portion the result of systematic errors, the persistence after several years of accurate analysis strongly hints at cracks in the standard cosmological scenario and the need for new physics. In this Letter of Interest we will focus on the $4.4\sigma$ tension between the Planck estimate of the Hubble constant $H_0$ and the SH0ES collaboration measurements. After showing the $H_0$ evaluations made from different teams using different methods and geometric calibrations, we will list a few interesting new physics models that could solve this tension and discuss how the next decade experiments will be crucial.

A precise measurement of the curvature of the Universe is of primeval importance for cosmology since it could not only confirm the paradigm of primordial inflation but also help in discriminating between different early Universe scenarios. The recent observations, while broadly consistent with a spatially flat standard $\Lambda$ Cold Dark Matter ($\Lambda$CDM) model, are showing tensions that still allow (and, in some cases, even suggest) a few percent deviations from a flat universe. In particular, the Planck Cosmic Microwave Background power spectra, assuming the nominal likelihood, prefer a closed universe at more than 99\% confidence level. While new physics could be in action, this anomaly may be the result of an unresolved systematic error or just a statistical fluctuation. However, since a positive curvature allows a larger age of the Universe, an accurate determination of the age of the oldest objects provides a smoking gun in confirming or falsifying the current flat $\Lambda$CDM model.

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 first-order approximation to a more realistic scenario that still needs to be fully understood. In this Letter of Interest we will list a few important goals that need to be addressed in the next decade, also taking into account the current discordances present between the different cosmological probes, as the Hubble constant $H_0$ value, the $\sigma_8 - S_8$ tension, and the anomalies present in the Planck results. Finally, we will give an overview of upgraded experiments and next-generation space-missions and facilities on Earth, that will be of crucial importance to address all these questions., Comment: Snowmass2021 - Letter of Interest

A precise measurement of the curvature of the Universe is of primeval importance for cosmology since it could not only confirm the paradigm of primordial inflation but also help in discriminating between different early Universe scenarios. The recent observations, while broadly consistent with a spatially flat standard $\Lambda$ Cold Dark Matter ($\Lambda$CDM) model, are showing tensions that still allow (and, in some cases, even suggest) a few percent deviations from a flat universe. In particular, the Planck Cosmic Microwave Background power spectra, assuming the nominal likelihood, prefer a closed universe at more than 99\% confidence level. While new physics could be in action, this anomaly may be the result of an unresolved systematic error or just a statistical fluctuation. However, since a positive curvature allows a larger age of the Universe, an accurate determination of the age of the oldest objects provides a smoking gun in confirming or falsifying the current flat $\Lambda$CDM model., Comment: Snowmass2021 - Letter of Interest

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 sensitivity a few statistically significant tensions between different independent cosmological datasets emerged. While these tensions can be in portion the result of systematic errors, the persistence after several years of accurate analysis strongly hints at cracks in the standard cosmological scenario and the need for new physics. In this Letter of Interest we will focus on the $4.4\sigma$ tension between the Planck estimate of the Hubble constant $H_0$ and the SH0ES collaboration measurements. After showing the $H_0$ evaluations made from different teams using different methods and geometric calibrations, we will list a few interesting new physics models that could solve this tension and discuss how the next decade experiments will be crucial., Comment: Snowmass2021 - Letter of Interest

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 information at the cost of increased modelling complexity with respect to previously analysed systems. We perform detailed modelling of the mass distribution for this lens system using three band Hubble Space Telescope imaging. We combine the measured time delays, line-of-sight central velocity dispersion of the deflector, and statistically constrained external convergence with our lens models to estimate two cosmological distances. We measure the ‘effective’ time-delay distance corresponding to the redshifts of the deflector and the lensed quasar DeffΔt=3382+146−115 Mpc and the angular diameter distance to the deflector Dd = 1711+376−280 Mpc, with covariance between the two distances. From these constraints on the cosmological distances, we infer the Hubble constant H0= 74.2+2.7−3.0 km s−1 Mpc−1 assuming a flat ΛCDM cosmology and a uniform prior for Ωm as Ωm∼U(0.05,0.5). This measurement gives the most precise constraint on H0 to date from a single lens. Our measurement is consistent with that obtained from the previous sample of six lenses analysed by the H0 Lenses in COSMOGRAIL’s Wellspring (H0LiCOW) collaboration. It is also consistent with measurements of H0 based on the local distance ladder, reinforcing the tension with the inference from early Universe probes, for example, with 2.2σ discrepancy from the cosmic microwave background measurement.

The standard $��$ Cold Dark Matter cosmological model provides a wonderful fit to current cosmological data, but a few tensions and anomalies became statistically significant with the latest data analyses. While these anomalies could be due to the presence of systematic errors in the experiments, they could also indicate the need for new physics beyond the standard model. In this Letter of Interest we focus on the tension of the Planck data with weak lensing measurements and redshift surveys, about the value of the matter energy density $��_m$, and the amplitude or rate of the growth of structure ($��_8,f��_8$). We list a few interesting models for solving this tension, and we discuss the importance of trying to fit with a single model a full array of data and not just one parameter at a time., Snowmass2021 - Letter of Interest

We present a measurement of the Hubble constant ($H_{0}$) and other cosmological parameters from a joint analysis of six gravitationally lensed quasars with measured time delays. All lenses except the first are analyzed blindly with respect to the cosmological parameters. In a flat $\Lambda$CDM cosmology, we find $H_{0} = 73.3_{-1.8}^{+1.7}$, a 2.4% precision measurement, in agreement with local measurements of $H_{0}$ from type Ia supernovae calibrated by the distance ladder, but in $3.1\sigma$ tension with $Planck$ observations of the cosmic microwave background (CMB). This method is completely independent of both the supernovae and CMB analyses. A combination of time-delay cosmography and the distance ladder results is in $5.3\sigma$ tension with $Planck$ CMB determinations of $H_{0}$ in flat $\Lambda$CDM. We compute Bayes factors to verify that all lenses give statistically consistent results, showing that we are not underestimating our uncertainties and are able to control our systematics. We explore extensions to flat $\Lambda$CDM using constraints from time-delay cosmography alone, as well as combinations with other cosmological probes, including CMB observations from $Planck$, baryon acoustic oscillations, and type Ia supernovae. Time-delay cosmography improves the precision of the other probes, demonstrating the strong complementarity. Allowing for spatial curvature does not resolve the tension with $Planck$. Using the distance constraints from time-delay cosmography to anchor the type Ia supernova distance scale, we reduce the sensitivity of our $H_0$ inference to cosmological model assumptions. For six different cosmological models, our combined inference on $H_{0}$ ranges from $\sim73$-$78~\mathrm{km~s^{-1}~Mpc^{-1}}$, which is consistent with the local distance ladder constraints., Comment: Accepted for publication in MNRAS; 23 pages, 13 figures, 8 tables

Many of the fundamental physical constants in Physics, as a discipline, are measured to exquisite levels of precision. The fundamental constants that define Cosmology, however, are largely determined via a handful of independent techniques that are applied to even fewer datasets. The history of the measurement of the Hubble Constant (H0), which serves to anchor the expansion history of the Universe to its current value, is an exemplar of the difficulties of cosmological measurement; indeed, as we approach the centennial of its first measurement, the quest for H0 still consumes a great number of resources. In this white paper, we demonstrate how the approaching era of Extremely Large Telescopes (ELTs) will transform the astrophysical measure of H0 from the limited and few into a fundamentally new regime where (i) multiple, independent techniques are employed with modest use of large aperture facilities and (ii) 1% or better precision is readily attainable. This quantum leap in how we approach H0 is due to the unparalleled sensitivity and spatial resolution of ELT's and the ability to use integral field observations for simultaneous spectroscopy and photometry, which together permit both familiar and new techniques to effectively by-pass the conventional 'ladder' framework to minimize total uncertainty. Three independent techniques are discussed -- (i) standard candles via a two-step distance ladder applied to metal, poor stellar populations, (ii) standard clocks via gravitational lens cosmography, and (iii) standard sirens via gravitational wave sources -- each of which can reach 1% with relatively modest investment from 30-m class facilities., Submitted as an Astro2020 White Paper. Please send comments to both Rachael Beaton & Simon Birrer. Development of this paper occurred as part of the The US Extremely Large Telescope Program Workshop in Oct 2018. We wish to acknowledge NOAO for bringing the co-authors together, in particular the enthusiasm and tireless leadership of Mark Dickinson

Strong-gravitational lens systems with quadruply-imaged quasars (quads) are unique probes to address several fundamental problems in cosmology and astrophysics. Although they are intrinsically very rare, ongoing and planned wide-field deep-sky surveys are set to discover thousands of such systems in the next decade. It is thus paramount to devise a general framework to model strong-lens systems to cope with this large influx without being limited by expert investigator time. We propose such a general modelling framework (implemented with the publicly available software Lenstronomy) and apply it to uniformly model three band Hubble Space Telescope Wide Field Camera 3 images of 12 quads. This is the largest uniformly modelled sample of quads to date and paves the way for a variety of studies. To illustrate the scientific content of the sample, we investigate the alignment between the mass and light distribution in the deflectors. The position angles of these distributions are well-aligned, except when there is strong external shear. However, we find no correlation between the ellipticity of the light and mass distributions. We also show that the observed flux-ratios between the images depart significantly from the predictions of simple smooth models. The departures are strongest in the bluest band, consistent with microlensing being the dominant cause in addition to millilensing. Future papers will exploit this rich dataset in combination with ground based spectroscopy and time delays to determine quantities such as the Hubble constant, the free streaming length of dark matter, and the normalization of the initial stellar mass function.

We present a measurement of the Hubble constant ($H_{0}$) and other cosmological parameters from a joint analysis of six gravitationally lensed quasars with measured time delays. All lenses except the first are analyzed blindly with respect to the cosmological parameters. In a flat $��$CDM cosmology, we find $H_{0} = 73.3_{-1.8}^{+1.7}$, a 2.4% precision measurement, in agreement with local measurements of $H_{0}$ from type Ia supernovae calibrated by the distance ladder, but in $3.1��$ tension with $Planck$ observations of the cosmic microwave background (CMB). This method is completely independent of both the supernovae and CMB analyses. A combination of time-delay cosmography and the distance ladder results is in $5.3��$ tension with $Planck$ CMB determinations of $H_{0}$ in flat $��$CDM. We compute Bayes factors to verify that all lenses give statistically consistent results, showing that we are not underestimating our uncertainties and are able to control our systematics. We explore extensions to flat $��$CDM using constraints from time-delay cosmography alone, as well as combinations with other cosmological probes, including CMB observations from $Planck$, baryon acoustic oscillations, and type Ia supernovae. Time-delay cosmography improves the precision of the other probes, demonstrating the strong complementarity. Allowing for spatial curvature does not resolve the tension with $Planck$. Using the distance constraints from time-delay cosmography to anchor the type Ia supernova distance scale, we reduce the sensitivity of our $H_0$ inference to cosmological model assumptions. For six different cosmological models, our combined inference on $H_{0}$ ranges from $\sim73$-$78~\mathrm{km~s^{-1}~Mpc^{-1}}$, which is consistent with the local distance ladder constraints., Accepted for publication in MNRAS; 23 pages, 13 figures, 8 tables

Strong gravitational lenses with measured time delay are a powerful tool to measure cosmological parameters, especially the Hubble constant ($H_0$). Recent studies show that by combining just three multiply-imaged AGN systems, one can determine $H_0$ to 2.4% precision. Furthermore, the number of time-delay lens systems is growing rapidly, enabling the determination of $H_0$ to 1% precision in the near future. However, as the precision increases it is important to ensure that systematic errors and biases remain subdominant. For this purpose, challenges with simulated datasets are a key component in this process. Following the experience of the past challenge on time delay, where it was shown that time delays can indeed be measured precisely and accurately at the sub-percent level, we now present the "Time Delay Lens Modeling Challenge" (TDLMC). The goal of this challenge is to assess the present capabilities of lens modeling codes and assumptions and test the level of accuracy of inferred cosmological parameters given realistic mock datasets. We invite scientists to model a set of simulated HST observations of 50 mock lens systems. The systems are organized in rungs, with the complexity and realism increasing going up the ladder. The goal of the challenge is to infer $H_0$ for each rung, given the HST images, the time delay, and stellar velocity dispersion of the deflector for a fixed background cosmology. The TDLMC challenge starts with the mock data release on 2018 January 8th. The deadline for blind submission is different for each rung. The deadline for Rung 0-1 is 2018 September 8; the deadline for Rung 2 is 2019 April 8 and the one for Rung 3 is 2019 September 8. This first paper gives an overview of the challenge including the data design, and a set of metrics to quantify the modeling performance and challenge details., 6 pages, 2 figures, submitted to MNRAS

We present a measurement of the Hubble constant (H-0) and other cosmological parameters from a joint analysis of six gravitationally lensed quasars with measured time delays. All lenses except the first are analysed blindly with respect to the cosmological parameters. In a flat Lambda cold dark matter (Lambda CDM) cosmology, we find H-0 = 73.3(-1.8)(+1.7) km s(-1) Mpc(-1), a 2.4 per cent precision measurement, in agreement with local measurements of H-0 from type Ia supernovae calibrated by the distance ladder, but in 3.1 sigma tension with Planck observations of the cosmic microwave background (CMB). This method is completely independent of both the supernovae and CMB analyses. A combination of time-delay cosmography and the distance ladder results is in 5.3 sigma tension with Planck CMB determinations of H-0 in flat Lambda CDM. We compute Bayes factors to verify that all lenses give statistically consistent results, showing that we are not underestimating our uncertainties and are able to control our systematics. We explore extensions to flat Lambda CDM using constraints from time-delay cosmography alone, as well as combinations with other cosmological probes, including CMB observations from Planck, baryon acoustic oscillations, and type Ia supernovae. Time-delay cosmography improves the precision of the other probes, demonstrating the strong complementarity. Allowing for spatial curvature does not resolve the tension with Planck. Using the distance constraints from time-delay cosmography to anchor the type Ia supernova distance scale, we reduce the sensitivity of our H-0 inference to cosmological model assumptions. For six different cosmological models, our combined inference on H-0 ranges from similar to 73 to 78 km s(-1) Mpc(-1), which is consistent with the local distance ladder constraints.

Strong-lensing time delays enable the measurement of the Hubble constant (H0) independently of other traditional methods. The main limitation to the precision of time-delay cosmography is mass-sheet degeneracy (MSD). Some of the previous TDCOSMO analyses broke the MSD by making standard assumptions about the mass density profile of the lens galaxy, reaching 2% precision from seven lenses. However, this approach could potentially bias the H0 measurement or underestimate the errors. For this work, we broke the MSD for the first time using spatially resolved kinematics of the lens galaxy in RXJ1131 1231 obtained from the Keck Cosmic Web Imager spectroscopy, in combination with previously published time delay and lens models derived from Hubble Space Telescope imaging. This approach allowed us to robustly estimate H0, e ffectively implementing a maximally flexible mass model. Following a blind analysis, we estimated the angular diameter distance to the lens galaxy Dd = 865 +85 81 Mpc and the time-delay distance D t = 2180 +472 271 Mpc, giving H0 = 77:1 +7:3 7:1 km s 1 Mpc 1 - for a flat cold dark matter cosmology. The error budget accounts for all uncertainties, including the MSD inherent to the lens mass profile and line-of-sight e ffects, and those related to the mass-anisotropy degeneracy and projection e ffects. Our new measurement is in excellent agreement with those obtained in the past using standard simply parametrized mass profiles for this single system (H0 = 78:3 +3:4 3:3 km s 1 Mpc 1) and for seven lenses (H0 = 74:2 +1:6 1:6 km s 1 Mpc 1), or for seven lenses using single-aperture kinematics and the same maximally flexible models used by us ( H0 = 73 :3+5:8 5:8 km s 1 Mpc 1). This agreement corroborates the methodology of time-delay cosmography.

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 first-order approximation to a more realistic scenario that still needs to be fully understood. In this Letter of Interest we will list a few important goals that need to be addressed in the next decade, also taking into account the current discordances present between the different cosmological probes, as the Hubble constant H-0 value, the sigma S-8(8) tension, and the anomalies present in the Planck results. Finally, we will give an overview of upgraded experiments and next-generation space-missions and facilities on Earth that will be of crucial importance to address all these questions. (C) 2021 Elsevier B.V. All rights reserved.

A precise measurement of the curvature of the Universe is of prime importance for cosmology since it could not only confirm the paradigm of primordial inflation but also help in discriminating between different early-Universe scenarios. Recent observations, while broadly consistent with a spatially flat standard Λ Cold Dark Matter ( Λ CDM) model, show tensions that still allow (and, in some cases, even suggest) a few percent deviations from a flat universe. In particular, the Planck Cosmic Microwave Background power spectra, assuming the nominal likelihood, prefer a closed universe at more than 99% confidence level. While new physics could be at play, this anomaly may be the result of an unresolved systematic error or just a statistical fluctuation. However, since positive curvature allows a larger age of the Universe, an accurate determination of the age of the oldest objects provides a smoking gun in confirming or falsifying the current flat Λ CDM model.

Full author list: A J Shajib, S Birrer, T Treu, A Agnello, E J Buckley-Geer, J H H Chan, L Christensen, C Lemon, H Lin, M Millon, J Poh, C E Rusu, D Sluse, C Spiniello, G C-F Chen, T Collett, F Courbin, C D Fassnacht, J Frieman, A Galan, D Gilman, A More, T Anguita, M W Auger, V Bonvin, R McMahon, G Meylan, K C Wong, T M C Abbott, J Annis, S Avila, K Bechtol, D Brooks, D Brout, D L Burke, A Carnero Rosell, M Carrasco Kind, J Carretero, F J Castander, M Costanzi, L N da Costa, J De Vicente, S Desai, J P Dietrich, P Doel, A Drlica-Wagner, A E Evrard, D A Finley, B Flaugher, P Fosalba, J García-Bellido, D W Gerdes, D Gruen, R A Gruendl, J Gschwend, G Gutierrez, D L Hollowood, K Honscheid, D Huterer, D J James, T Jeltema, E Krause, N Kuropatkin, T S Li, M Lima, N MacCrann, M A G Maia, J L Marshall, P Melchior, R Miquel, R L C Ogando, A Palmese, F Paz-Chinchón, A A Plazas, A K Romer, A Roodman, M Sako, E Sanchez, B Santiago, V Scarpine, M Schubnell, D Scolnic, S Serrano, I Sevilla-Noarbe, M Smith, M Soares-Santos, E Suchyta, G Tarle, D Thomas, A R Walker, Y Zhang, 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 information at the cost of increased modelling complexity with respect to previously analysed systems. We perform detailed modelling of the mass distribution for this lens system using three band Hubble Space Telescope imaging. We combine the measured time delays, line-of-sight central velocity dispersion of the deflector, and statistically constrained external convergence with our lens models to estimate two cosmological distances. We measure the 'effective' time-delay distance corresponding to the redshifts of the deflector and the lensed quasar DΔ t eff=3382-115+146 Mpc and the angular diameter distance to the deflector Dd = 1711-280+376 Mpc, with covariance between the two distances. From these constraints on the cosmological distances, we infer the Hubble constant H0= 74.2-3.0+2.7 km s-1 Mpc-1 assuming a flat ΛCDM cosmology and a uniform prior for ωm as \Omega m ∼ \mathcal {U(0.05, 0.5). This measurement gives the most precise constraint on H0 to date from a single lens. Our measurement is consistent with that obtained from the previous sample of six lenses analysed by the H0 Lenses in COSMOGRAIL's Wellspring (H0LiCOW) collaboration. It is also consistent with measurements of H0 based on the local distance ladder, reinforcing the tension with the inference from early Universe probes, for example, with 2.2σ discrepancy from the cosmic microwave background measurement., TT acknowledges support by the Packard Foundation through a Packard Research fellowship and by the National Science Foundation through NSF grants AST-1714953 and AST-1906976. This project is partly funded by the Danish council for independent research under the project ‘Fundamentals of Dark Matter Structures’, DFF - 6108-00470. AA was supported by a grant from VILLUM FONDEN (project number 16599). JHHC, MM, CL, DS, FC, and AG acknowledge support from the Swiss National Science Foundation (SNSF) and by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program (COSMICLENS: grant agreement No 787866). CS has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie actions grant agreement No 664931. GCFC acknowledges support from the Ministry of Education in Taiwan via Government Scholarship to Study Abroad (GSSA). CDF and GCFC acknowledge support for this work from the National Science Foundation under Grant No AST-1715611. TA acknowledges support from Proyecto FONDECYT N○ 1190335. KCW was supported by World Premier International Research Center Initiative (WPI Initiative), MEXT, Japan. This work used computational and storage services associated with the Hoffman2 Shared Cluster provided by UCLA Institute for Digital Research and Education’s Research Technology Group. This work used the Extreme Science and Engineering Discovery Environment (XSEDE) through allocation TG-AST190038, which is supported by National Science Foundation grant number ACI-1548562 (Towns et al. 2014). Specifically, this work used the Comet and Oasis system at the San Diego Supercomputer Center (SDSC), and the Bridges system, which is supported by NSF award number ACI-1445606, at the Pittsburgh Supercomputing Center (PSC, Nystrom et al. 2015). AJS thanks Smadar Naoz for providing access to additional computing nodes on the Hoffman2 Shared Cluster and Khalid Jawed for assisting with additional computational resources from the Structures–Computer Interaction Laboratory at UCLA. The DES data management system is supported by the National Science Foundation under Grant Numbers AST-1138766 and AST-1536171. The DES participants from Spanish institutions are partially supported by MINECO under grants AYA2015-71825, ESP2015-66861, FPA2015-68048, SEV-2016-0588, SEV-2016-0597, and MDM-2015-0509, some of which include ERDF funds from the European Union. IFAE is partially funded by the CERCA program of the Generalitat de Catalunya. Research leading to these results has received funding from the European Research Council under the European Union’s Seventh Framework Program (FP7/2007-2013) including ERC grant agreements 240672, 291329, and 306478. We acknowledge support from the Australian Research Council Centre of Excellence for All-sky Astrophysics (CAASTRO), through project number CE110001020, and the Brazilian Instituto Nacional de Ciência e Tecnologia (INCT) e-Universe (CNPq grant 465376/2014-2).

The DES Collaboration: et al., In time-delay cosmography, three of the key ingredients are (1) determining the velocity dispersion of the lensing galaxy, (2) identifying galaxies and groups along the line of sight with sufficient proximity and mass to be included in the mass model, and (3) estimating the external convergence κext from less massive structures that are not included in the mass model. We present results on all three of these ingredients for two time-delay lensed quad quasar systems, DES J0408–5354 and WGD 2038–4008 . We use the Gemini, Magellan, and VLT telescopes to obtain spectra to both measure the stellar velocity dispersions of the main lensing galaxies and to identify the line-of-sight galaxies in these systems. Next, we identify 10 groups in DES J0408–5354 and two groups in WGD 2038–4008 using a group-finding algorithm. We then identify the most significant galaxy and galaxy-group perturbers using the ‘flexion shift’ criterion. We determine the probability distribution function of the external convergence κext for both of these systems based on our spectroscopy and on the DES-only multiband wide-field observations. Using weighted galaxy counts, calibrated based on the Millennium Simulation, we find that DES J0408–5354 is located in a significantly underdense environment, leading to a tight (width ∼3 per cent⁠), negative-value κext distribution. On the other hand, WGD 2038–4008 is located in an environment of close to unit density, and its low source redshift results in a much tighter κext of ∼1 per cent⁠, as long as no external shear constraints are imposed., JP would like to thank Gourav Khullar for his help and insightful discussions that helped improve the analysis in this paper. This work made use of computing resources and support provided by the Research Computing Center at the University of Chicago. JP is supported in part by the Kavli Institute for Cosmological Physics at the University of Chicago through grant NSF PHY-1125897 and an endowment from the Kavli Foundation and its founder Fred Kavli. AJS was supported by the National Aeronautics and Space Administration (NASA) through the Space Telescope Science Institute (STScI) grant HST-GO-15320. AJS was also supported by the Dissertation Year Fellowship from the University of California, Los Angeles (UCLA) graduate division. TA acknowledges support from Proyecto FONDECYT N: 1190335. This work was supported by World Premier International Research Center Initiative (WPI Initiative), MEXT, Japan. CDF acknowledges support for this work from the National Science Foundation under Grant No. AST-1715611. SM acknowledges the funding from the European Research Council (ERC) under the EUs Horizon 2020 research and innovation program (COSMICLENS; grant agreement No. 787886). Funding for the DES Projects has been provided by the U.S. Department of Energy, the U.S. National Science Foundation, the Ministry of Science and Education of Spain, the Science and Technology Facilities Council of the United Kingdom, the Higher Education Funding Council for England, the National Center for Supercomputing Applications at the University of Illinois at Urbana-Champaign, the Kavli Institute of Cosmological Physics at the University of Chicago, the Center for Cosmology and Astro-Particle Physics at the Ohio State University, the Mitchell Institute for Fundamental Physics and Astronomy at Texas A&M University, Financiadora de Estudos e Projetos, Fundação Carlos Chagas Filho de Amparo à Pesquisa do Estado do Rio de Janeiro, Conselho Nacional de Desenvolvimento Científico e Tecnológico and the Ministério da Ciência, Tecnologia e Inovação, the Deutsche Forschungsgemeinschaft and the Collaborating Institutions in the Dark Energy Survey. The Collaborating Institutions are Argonne National Laboratory, the University of California at Santa Cruz, the University of Cambridge, Centro de Investigaciones Energéticas, Medioambientales y Tecnológicas-Madrid, the University of Chicago, University College London, the DES-Brazil Consortium, the University of Edinburgh, the Eidgenössische Technische Hochschule (ETH) Zürich, Fermi National Accelerator Laboratory, the University of Illinois at Urbana-Champaign, the Institut de Ciències de l’Espai (IEEC/CSIC), the Institut de Física d’Altes Energies, Lawrence Berkeley National Laboratory, the Ludwig-Maximilians Universität München and the associated Excellence Cluster Universe, the University of Michigan, the National Optical Astronomy Observatory, the University of Nottingham, The Ohio State University, the University of Pennsylvania, the University of Portsmouth, SLAC National Accelerator Laboratory, Stanford University, the University of Sussex, Texas A&M University, and the OzDES Membership Consortium. Based in part on observations at Cerro Tololo Inter-American Observatory, National Optical Astronomy Observatory, which is operated by the Association of Universities for Research in Astronomy (AURA) under a cooperative agreement with the National Science Foundation. The DES data management system is supported by the National Science Foundation under Grant Numbers AST-1138766 and AST-1536171. The DES participants from Spanish institutions are partially supported by MINECO under grants AYA2015-71825, ESP2015-88861, FPA2015-68048, SEV-2012-0234, SEV-2016-0597, and MDM-2015-0509, some of which include ERDF funds from the European Union. IFAE is partially funded by the CERCA program of the Generalitat de Catalunya. Research leading to these results has received funding from the European Research Council under the European Union’s Seventh Framework Program (FP7/2007-2013) including ERC grant agreements 240672, 291329, and 306478. We acknowledge support from the Australian Research Council Centre of Excellence for All-sky Astrophysics (CAASTRO), through project number CE110001020. This manuscript has been authored by Fermi Research Alliance, LLC under Contract No. DE-AC02-07CH11359 with the U.S. Department of Energy, Office of Science, Office of High Energy Physics. The United States Government retains and the publisher, by accepting the article for publication, acknowledges that the United States Government retains a non-exclusive, paid-up, irrevocable, world-wide license to publish or reproduce the published form of this manuscript, or allow others to do so, for United States Government purposes.