Time-delay strong lensing provides a unique way to directly measure the Hubble constant ( H _ { 0 } ) .
The precision of the H _ { 0 } measurement depends on the uncertainties in the time-delay measurements , the mass distribution of the main deflector ( s ) , and the mass distribution along the line of sight . \citet TieKochanek18 have proposed a new microlensing effect on time delays based on differential magnification of the coherent accretion disc variability of the lensed quasar .
If real , this effect could significantly broaden the uncertainty on the time delay measurements by up to 30 % for lens systems such as PG 1115 + 080 , which have relatively short time delays and monitoring over several different epochs .
In this paper we develop a new technique that uses the cosmological time-delay ratios and simulated microlensing maps within a Bayesian framework in order to limit the allowed combinations of microlensing delays and thus to lessen the uncertainties due to the proposed effect .
We show that , under the assumption of \citet TieKochanek18 , the uncertainty on the time-delay distance ( { D _ { \Delta t } } , which is proportional to 1/ H _ { 0 } ) of short time-delay ( \sim 18 days ) lens , PG 1115 + 080 , increases from \sim 7 % to \sim 10 % by simultaneously fitting the three time-delay measurements from the three different datasets across twenty years , while in the case of long time-delay ( \sim 90 days ) lens , the microlensing effect on time delays is negligible as the uncertainty on { D _ { \Delta t } } of RXJ 1131 - 1231 only increases from \sim 2.5 % to \sim 2.6 % .