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      <Title>Systematics in H_0 from lensing: a comprehensive study of internal structure in elliptical galaxies</Title>
      
      <Abstract>Recently, there has been a strong tension between different measurements of the Hubble constant, H_0. If systematics can be ruled out in these measurements, then this discrepancy will point to new physics either beyond the standard Lambda cold dark matter cosmology, or beyond our current understanding of the galactic/stellar astrophysics. Time-delay cosmography has provided a competitive measurement of H_0 with ~2% uncertainty combining only seven lens systems. However, if the true mass distribution deviates from the power law, the assumption of a power-law mass distribution in the lens galaxies can be a source of systematic in the measured H_0. We will analyze a large sample of galaxy-galaxy lenses that is representative of the time-delay lens population to study the internal structure of the elliptical lens galaxies. We will identify if the mass distribution in these galaxies deviate from (or closely follow) the power law and thus the presence (or absence) of systematic biases in the reported H_0 values from time-delay cosmography. Furthermore, we will provide tight empirical priors for elliptical galaxy structural parameters for use in future time-delay lens analyses.</Abstract>
      
      <PrincipalInvestigator
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         FirstName="Anowar"
         MiddleInitial="J"
         LastName="Shajib"
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         Institution="University of California - Los Angeles"
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         Honorific="Dr."
         FirstName="Joshua"
         LastName="Frieman"
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         Institution="Stanford University"
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         Institution="University of Copenhagen, Niels Bohr Institute"
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         FirstName="Alessandro"
         LastName="Sonnenfeld"
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      <TeamExpertise>Our team includes experts in state-of-the-art lens modeling. A. Shajib has carried out uniform modeling of the largest sample of lensed quasars (N=13) using multi-band HST imaging [1]. Shajib proposed the efficient computational method that we will apply in this analysis to model the lens mass distribution of non-analytical profiles, such as the elliptical cored generalized-NFW profile or the elliptical Sersic profile [2]. Moreover, Shajib has modeled one time-delay lens [3] and S. Birrer has modeled two time-delay lenses [4, 5] to the requirement of cosmographic detail to measure the Hubble constant. Birrer is the lead developer and Shajib is the contributing developer of the state-of-the-art lens modeling software "lenstronomy", which we will use in this analysis [6].

T. Treu and A. Sonnenfeld both played integral roles in the SLACS and SL2S surveys, from which we will use the HST data in this study [7, 8, 9, 10, 11].

References:
1. Shajib, Birrer, Treu, Agnello, Frieman et al. 2019. Is every strong lens model unhappy in its own way? Uniform modelling of a sample of 13 quadruply+ imaged quasars. MNRAS, Volume 483, Issue 4, p.5649-5671.
2. Shajib 2019. Unified lensing and kinematic analysis for any elliptical mass profile. MNRAS, Volume 488, Issue 1, p.1387-1400.
3. Shajib, Birrer, Treu, Agnello, Frieman et al. 2019. STRIDES: A 3.9 per cent measurement of the Hubble constant from the strong lens system DES J0408-5354. arXiv:1910.06306. 
4. Birrer, Amara &amp; Refregier 2016. The mass-sheet degeneracy and time-delay cosmography: analysis of the strong lens RXJ1131-1231. JCAP, Issue 08, article id. 020.
5. Birrer, Treu, Agnello, Shajib et al. 2019. H0LiCOW - IX. Cosmographic analysis of the doubly imaged quasar SDSS 1206+4332 and a new measurement of the Hubble constant. MNRAS, Volume 484, Issue 4, p.4726-4753.
6. Birrer &amp; Amara 2018. lenstronomy: Multi-purpose gravitational lens modelling software package, Physics of the Dark Universe, 22, 189.
7. Treu et al. 2006. The Sloan Lens ACS Survey. II. Stellar Populations and Internal Structure of Early-Type Lens Galaxies. ApJ, Volume 640, Issue 2, pp. 662-672.
8. Treu et al. 2009. The SLACS Survey. VIII. The Relation between Environment and Internal Structure of Early-Type Galaxies. ApJ, Volume 690, Issue 1, pp. 670-682.
9. Sonnenfeld, Treu et al. 2013. The SL2S Galaxy-scale Lens Sample. III. Lens Models, Surface Photometry, and Stellar Masses for the Final Sample. ApJ, Volume 777, Issue 2, article id. 97, 13 pp.
10. Sonnenfeld, Treu et al. 2013. The SL2S Galaxy-scale Lens Sample. IV. The Dependence of the Total Mass Density Profile of Early-type Galaxies on Redshift, Stellar Mass, and Size. ApJ, Volume 777, Issue 2, article id. 98, 15 pp.
11. Sonnenfeld, Treu et al. 2015. The SL2S Galaxy-scale Lens Sample. V. Dark Matter Halos and Stellar IMF of Massive Early-type Galaxies Out to Redshift 0.8. ApJ, Volume 800, Issue 2, article id. 94, 22 pp.</TeamExpertise>
      
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