Cosmology From Gravitational Lens Time Delays and Planck Data

Abstract

Under the assumption of a flat ΛCDM cosmology, recent data from the Planck satellite point toward a Hubble constant that is in tension with that measured by gravitational lens time delays and by the local distance ladder. Prosaically, this difference could arise from unknown systematic uncertainties in some of the measurements. More interestingly -if systematics were ruled out -resolving the tension would require a departure from the flat ΛCDM cosmology, introducing for example a modest amount of spatial curvature, or a non-trivial dark energy equation of state. To begin to address these issues, we present here an analysis of the gravitational lens RXJ1131−1231 that is improved in one particular regard: we examine the issue of systematic error introduced by an assumed lens model density profile. We use more flexible gravitational lens models with baryonic and dark matter components, and find that the exquisite Hubble Space Telescope image with thousands of intensity pixels in the Einstein ring and the stellar velocity dispersion of the lens contain sufficient information to constrain these more flexible models. The total uncertainty on the time-delay distance is 6.6% for a single system. We proceed to combine our improved time-delay distance measurements with the WMAP9 and Planck posteriors. In an open ΛCDM model, the data for RXJ1131−1231 in combination with Planck favor a flat universe with Ω k = 0.00 +0.01 −0.02 (68% CI). In a flat wCDM model, the combination of RXJ1131−1231 and Planck yields w = −1.52 +0.19 −0.20 (68% CI).

Sn Refsdal: Photometry and Time Delay Measurements of the First Einstein Cross Supernova

“…After accounting for the difference in the gravitational potential traversed by the light path for each multiple image (Shapiro 1964), the time delay can be used to directly constrain the Hubble constant (Refsdal 1964) and other cosmological parameters  (Linder 2004(Linder , 2011Coe & Moustakas 2009). Distant quasars multiply-imaged by foreground galaxies have been used for such time delay cosmography measurements, providing valuable cosmological constraints that can complement or validate other methods such as Type Ia SNe, baryon acoustic oscillations and the cosmic microwave background (e.g., Saha et al 2006;Oguri 2007;Coles 2008;Suyu et al 2010Suyu et al , 2013Suyu et al , 2014; and see Treu & Ellis 2014 for a recent review). Figure 9.…”

Discovery of two gravitationally lensed quasars in the Dark Energy Survey

“…Schechter et al 1997;Tewes et al 2013) that depends on the cosmological distances to the lens and the source and the gravitational potential of the lens (Refsdal 1964). This enables one-step measurements of the expansion history of the Universe and the dark matter halos of the massive galaxies that act as deflectors (e.g., Suyu et al 2014). The microlensing effect on the multiple quasar images, induced by stars in the deflector, provides a quantitative handle on the stellar content of the lens galaxies (e.g., Schechter & Wambsganss 2002;Oguri, Rusu & Falco 2014;Schechter et al 2014;Jiménez-Vicente et al 2015), and can simultaneously provide constraints on the inner structure of the lensed quasar, both the accretion disk size and the thermal profile (e.g.…”

Tailoring strong lensing cosmographic observations

“…For the lens part of the Fermat potential, the lens mass modeling requires constraint by measurement of the galaxy velocity dispersion through spectroscopy. This also plays a key role in breaking the mass sheet degeneracy [9,24,25]. Similarly, spectroscopy obtains the redshifts of lens and source.…”

“…There is also a mass sheet degeneracy due to mass along the line of sight. Both these effects can be incorporated through [9] …”

“…Cosmic redshift drift has been recognized since the 1960s as a potential cosmographic probe, though not yet measured [3][4][5][6]. The strong gravitational lensing time delay distance-redshift relation was also proposed in the 1960s [7] and in the last few years has matured to the stage of being used as a cosmological probe [8,9].…”