Abstract
Abstract Strongly lensed quasars with time-delay measurements are well known to provide the “time-delay distances” , and the angular diameter distances to the lens galaxies D L . These two kinds of distances give stringent constraints on cosmological parameters. In this work, we explore a different use of time-delay observables: under the assumption of a flat universe, strong lensing observations can accurately measure the angular diameter distances to the sources D S . The corresponding redshifts of the quasars may be up to z S ∼ 4 according to the forecast. The high-redshift distances would sample the Hubble diagram between SNe Ia and the cosmic microwave background, model-independently providing direct information on the evolution of the nature of our universe, for example, the dark energy equation of state parameter w(z). We apply our method to the existing lensing system SDSS 1206+4332 and get at z S = 1.789. We also make a forecast for the era of Large Synoptic Survey Telescope. The uncertainty of D S depends on the redshifts of the lens and the source, the uncertainties of D Δt and D L , and the correlation between D Δt and D L . Larger correlation would result in tighter D S determination.
Highlights
In the standard cosmological model, i.e., ΛCDM, the Universe is flat, dominated by cold dark matter and dark energy with Equation-of-State (EoS) parameter w ≡ −1 (Frieman et al 2008)
According to the theory of strong gravitational lensing (Refsdal 1964; Treu 2010; Treu & Marshall 2016; Liao 2019), the arriving time difference between two images of the source measured from Active Galactic Nucleus (AGN) light curves is related with the geometry of the Universe and the gravity field of lens galaxy through:
We propose to measure the angular diameter distances to quasars at high redshifts with strong lensing and apply the method to SDSS 1206+4332
Summary
In the standard cosmological model, i.e., ΛCDM, the Universe is flat, dominated by cold dark matter and dark energy with Equation-of-State (EoS) parameter w ≡ −1 (Frieman et al 2008). Quasars at redshifts up to z ∼ 5 were proposed to measure the luminosity distances with a method based on X-ray and ultraviolet emission (Risaliti & Lusso 2019). Note that unlike SNe Ia which determine the relative distances, the strong lensing measures the absolute angular diameter distances, with which one can directly establish the Hubble diagram This approach is limited by the relatively low redshifts of the lenses z < 1.2 (Jee et al 2016). Motivated by acquiring high-redshift data for studying the Universe, we propose a method to measure the distances to quasars based on strong lensing.
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