Overconstrained gravitational lens models and the Hubble constant

Abstract

It is well known that measurements of H 0 from gravitational lens time delays scale as H 0 ∝ 1 − κ E where κ E is the mean convergence at the Einstein radius R E but that all available lens data other than the delays provide no direct constraints on κ E . The properties of the radial mass distribution constrained by lens data are R E and the dimensionless quantityis the second derivative of the deflection profile at R E . Lens models with too few degrees of freedom, like power law models with densities ρ ∝ r −n , have a one-to-one correspondence between ξ and κ E (for a power law model, ξ = 2(n − 2) and κ E = (3 − n)/2 = (2 − ξ)/4). This means that highly constrained lens models with few parameters quickly lead to very precise but inaccurate estimates of κ E and hence H 0 . Based on experiments with a broad range of plausible dark matter halo models, it is unlikely that any current estimates of H 0 from gravitational lens time delays are more accurate than ∼ 10%, regardless of the reported precision.

Constraining early dark energy with large-scale structure

“…The model parameters are given in Eqs. (7) and (8) for EDE and ΛCDM, respectively, corresponding to the best-fit parameters from Ref. [40] in the fit to primary CMB, CMB lensing, BAO, RSD, SNIa, and SH0ES data.…”

“…For example, the physical cold dark matter density ω cdm increases by over 5% when going from ΛCDM to EDE best-fit parameters [see Eqs. (7) and (8)]. This increase is needed to compensate for the early-ISWinduced growth suppression caused by the EDE.…”

“…We perform Markov-chain Monte Carlo (MCMC) analyses, sampling from the posterior distributions using the Metropolis-Hastings algorithm [73][74][75], with a Gelman-Rubin [76] convergence criterion R − 1 < 0.15 (unless otherwise stated). 7 We analyze the MCMC chains using both MontePython and GetDist [77], 8 which give very similar results.…”

“…2 However, some concerns about unaccounted systematics in lensing time-delay measurements have been raised, for instance in Refs. [7,8]; indeed, the latest strong-lensing analyses, after accounting for these systematics, have now found a lower value of H 0 with significantly increased error bars, H 0 ¼ 67.4 þ4.1 −3.2 km=s=Mpc [9]. 3 An additional fourth parameter, n, denoting an exponent of the scalar field potential V ∝ ð1 − cos θÞ n , can be included, and is only weakly constrained; the best-fit integer value is n ¼ 3 [26].…”

Galaxy mass profiles from strong lensing II: The elliptical power-law model

“…Wong et al 2020). A number of authors have suggested that the currently employed SPL model lacks the freedom necessary to model accurately the lens mass when measuring H 0 (Xu et al 2016;Sonnenfeld 2018;Kochanek 2020). The consequence could be that measurements of H 0 , although precise, are inaccurate because of a biased measurement of the potential at the positions of the lensed images.…”