In 2016 , the first strongly lensed Type Ia supernova , iPTF16geu at redshift z = 0.409 with four resolved images arranged symmetrically around the lens galaxy at z = 0.2163 , was discovered .
Here , refined observations of iPTF16geu , including the time delay between images , are used to decrease uncertainties in the lens model , including the the slope of the projected surface density of the lens galaxy , \Sigma \propto r ^ { 1 - \eta } , and to constrain the universal expansion rate H _ { 0 } .
Imaging with HST provides an upper limit on the slope \eta , in slight tension with the steeper density profiles indicated by imaging with Keck after iPTF16geu had faded , potentially due to dust extinction not corrected for in host galaxy imaging .
Since smaller \eta implies larger magnifications , we take advantage of the standard candle nature of Type Ia supernovae constraining the image magnifications , to obtain an independent constraint of the slope .
We find that a smooth lens density fails to explain the iPTF16geu fluxes , regardless of the slope , and additional sub-structure lensing is needed .
The total probability for the smooth halo model combined with star microlensing to explain the iPTF16geu image fluxes is maximized at 12 \% for \eta \sim 1.8 , in excellent agreement with Keck high spatial resolution data , and flatter than an isothermal halo .
It also agrees perfectly with independent constraints on the slope from lens velocity dispersion measurements .
Combining with the observed time delays between the images , we infer a lower bound on the Hubble constant , H _ { 0 } \gtrsim 40 { km s ^ { -1 } Mpc ^ { -1 } } at 68.3 \% confidence level .