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Register a new userTDCOSMO IV: Hierarchical time-delay cosmography -- joint inference of the Hubble constant and galaxy density profiles
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The H0LiCOW collaboration inferred via gravitational lensing time delays a Hubble constant $H_0=73.3^{+1.7}_{-1.8}$ km s$^{-1}{rm Mpc}^{-1}$, describing deflector mass density profiles by either a power-law or stars plus standard dark matter halos. The mass-sheet transform (MST) that leaves the lensing observables unchanged is considered the dominant source of residual uncertainty in $H_0$. We quantify any potential effect of the MST with flexible mass models that are maximally degenerate with H0. Our calculation is based on a new hierarchical approach in which the MST is only constrained by stellar kinematics. The approach is validated on hydrodynamically simulated lenses. We apply the method to the TDCOSMO sample of 7 lenses (6 from H0LiCOW) and measure $H_0=74.5^{+5.6}_{-6.1}$ km s$^{-1}{rm Mpc}^{-1}$. In order to further constrain the deflector mass profiles, we then add imaging and spectroscopy for 33 strong gravitational lenses from the SLACS sample. For 9 of the SLAC lenses we use resolved kinematics to constrain the stellar anisotropy. From the joint analysis of the TDCOSMO+SLACS sample, we measure $H_0=67.4^{+4.1}_{-3.2}$ km s$^{-1}{rm Mpc}^{-1}$, assuming that the TDCOSMO and SLACS galaxies are drawn from the same parent population. The blind H0LiCOW, TDCOSMO-only and TDCOSMO+SLACS analyses are in mutual statistical agreement. The TDCOSMO+SLACS analysis prefers marginally shallower mass profiles than H0LiCOW or TDCOSMO-only. While our new analysis does not statistically invalidate the mass profile assumptions by H0LiCOW, and thus their $H_0$ measurement relying on those, it demonstrates the importance of understanding the mass density profile of elliptical galaxies. The uncertainties on $H_0$ derived in this paper can be reduced by physical or observational priors on the form of the mass profile, or by additional data, chiefly spatially resolved kinematics of lens galaxies.
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Time-delay cosmography with gravitationally lensed quasars plays an important role in anchoring the absolute distance scale and hence measuring the Hubble constant, $H_{0}$, independent of traditional distance ladder methodology. A current potential limitation of time delay distance measurements is the mass-sheet transformation (MST) which leaves the lensed imaging unchanged but changes the distance measurements and the derived value of $H_0$. In this work we show that the standard method of addressing the MST in time delay cosmography, through a combination of high-resolution imaging and the measurement of the stellar velocity dispersion of the lensing galaxy, depends on the assumption that the ratio, $D_{rm s}/D_{rm ds}$, of angular diameter distances to the background quasar and between the lensing galaxy and the quasar can be constrained. This is typically achieved through the assumption of a particular cosmological model. Previous work (TDCOSMO IV) addressed the mass-sheet degeneracy and derived $H_{0}$ under the assumption of $Lambda$CDM model. In this paper we show that the mass sheet degeneracy can be broken without relying on a specific cosmological model by combining lensing with relative distance indicators such as supernovae type Ia and baryon acoustic oscillations, which constrain the shape of the expansion history and hence $D_{rm s}/D_{rm ds}$. With this approach, we demonstrate that the mass-sheet degeneracy can be constrained in a cosmological-model-independent way, and hence model-independent distance measurements in time-delay cosmography under mass-sheet transformations can be obtained.
Time-delay cosmography of lensed quasars has achieved 2.4% precision on the measurement of the Hubble constant, $H_0$. As part of an ongoing effort to uncover and control systematic uncertainties, we investigate three potential sources: 1- stellar kinematics, 2- line-of-sight effects, and 3- the deflector mass model. To meet this goal in a quantitative way, we reproduced the H0LiCOW/SHARP/STRIDES (hereafter TDCOSMO) procedures on a set of real and simulated data, and we find the following. First, stellar kinematics cannot be a dominant source of error or bias since we find that a systematic change of 10% of measured velocity dispersion leads to only a 0.7% shift on $H_0$ from the seven lenses analyzed by TDCOSMO. Second, we find no bias to arise from incorrect estimation of the line-of-sight effects. Third, we show that elliptical composite (stars + dark matter halo), power-law, and cored power-law mass profiles have the flexibility to yield a broad range in $H_0$ values. However, the TDCOSMO procedures that model the data with both composite and power-law mass profiles are informative. If the models agree, as we observe in real systems owing to the bulge-halo conspiracy, $H_0$ is recovered precisely and accurately by both models. If the two models disagree, as in the case of some pathological models illustrated here, the TDCOSMO procedure either discriminates between them through the goodness of fit, or it accounts for the discrepancy in the final error bars provided by the analysis. This conclusion is consistent with a reanalysis of six of the TDCOSMO (real) lenses: the composite model yields $74.0^{+1.7}_{-1.8}$ $km.s^{-1}.Mpc^{-1}$, while the power-law model yields $H_0=74.2^{+1.6}_{-1.6}$ $km.s^{-1}.Mpc^{-1}$. In conclusion, we find no evidence of bias or errors larger than the current statistical uncertainties reported by TDCOSMO.
Gravitational time delays, observed in strong lens systems where the variable background source is multiply-imaged by a massive galaxy in the foreground, provide direct measurements of cosmological distance that are very complementary to other cosmographic probes. The success of the technique depends on the availability and size of a suitable sample of lensed quasars or supernovae, precise measurements of the time delays, accurate modeling of the gravitational potential of the main deflector, and our ability to characterize the distribution of mass along the line of sight to the source. We review the progress made during the last 15 years, during which the first competitive cosmological inferences with time delays were made, and look ahead to the potential of significantly larger lens samples in the near future.
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 the Hubble constant and post-Newtonian parameter are incorporated in two distance ratios which reflect the lensing mass and dynamical mass, respectively. Through the reanalysis of the four publicly released lenses distance posteriors from the H0LiCOW collaboration, the simultaneous constraints of Hubble constant and post-Newtonian parameter are obtained. Our results suggests no deviation from the General Relativity, $gamma_{texttt{PPN}}=0.87^{+0.19}_{-0.17}$ with a Hubble constant favors 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 are able to reach the order of $7.7%$ for the post-Newtonian parameter and $1.4%$ for Hubble constant.
We use supernovae measurements, calibrated by the local determination of the Hubble constant $H_0$ by SH0ES, to interpolate the distance-redshift relation using Gaussian process regression. We then predict, independent of the cosmological model, the distances that are measured with strong lensing time delays. We find excellent agreement between these predictions and the measurements. The agreement holds when we consider only the redshift dependence of the distance-redshift relation, independent of the value of $H_0$. Our results disfavor the possibility that lens mass modeling contributes a 10% bias or uncertainty in the strong lensing analysis, as suggested recently in the literature. In general our analysis strengthens the case that residual systematic errors in both measurements are below the level of the current discrepancy with the CMB determination of $H_0$, and supports the possibility of new physical phenomena on cosmological scales. With additional data our methodology can provide more stringent tests of unaccounted for systematics in the determinations of the distance-redshift relation in the late universe.
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