The distance sum rule from strong lensing systems and quasars – test of cosmic curvature and beyond

Abstract

Testing the distance-sum-rule in strong lensing systems provides an interesting method to determine the curvature parameter Ω k using more local objects. In this paper, we apply this method to a quite recent data set of strong lensing systems in combination with intermediate-luminosity quasars calibrated as standard rulers. In the framework of three types of lens models extensively used in strong lensing studies (SIS model, power-law spherical model, and extended power-law lens model), we show that the assumed lens model has a considerable impact on the cosmic curvature constraint, which is found to be compatible or marginally compatible with the flat case (depending on the lens model adopted). Analysis of low, intermediate and high-mass sub-samples defined according to the lens velocity dispersion demonstrates that, although it is not reasonable to characterize all lenses with a uniform model, such division has little impact on cosmic curvature inferred. Finally, thinking about future when massive surveys will provide their yields, we simulated a mock catalog of strong lensing systems expected to be seen by the LSST, together with a realistic catalog of quasars. We found that with about 16000 such systems, combined with the distance information provided by 500 compact milliarcsecond radio sources seen in future radio astronomical surveys, one would be able to constrain the cosmic curvature with an accuracy of ∆Ω k ≃ 10 −3 , which is comparable to the precision of Planck 2015 results.

Model-independent Estimations for the Cosmic Curvature from the Latest Strong Gravitational Lensing Systems

“…Therefore, more well-measured strong lensing events might be very useful for reducing the bias in estimation of curvature. In this sense, analyzing simulated SGL observations from Large Synoptic Survey Telescope (LSST) can give some predictions for constraints on cosmological parameters (Collett 2015;Cao et al 2018;Qi et al 2018;Ma et al 2019). Qi et al (2018) have found that, combining about 16000 strong lensing events combined with the distance information provided by 500 compact radio quasars, one can constrain the cosmic curvature with an accuracy of Ω k 10 −3 , which is comparable to the precision of Planck 2015 results.…”

“…Our procedure follows the phenomenological model which quantifies the luminosity L and redshift z dependence of the linear sizes of quasars as (Gurvtis. 1994;Gurvtis et al 1999;Cao et al 2017a;Qi et al 2018)…”

“…The parameter β(r) = 1 − σ 2 θ /σ 2 r denotes the anisotropy of the stellar velocity dispersion, and is also called as the stellar orbital anisotropy, where σ θ and σ r are the tangential and radial velocity dispersions, respectively. In the literature, β is usually assumed independent of r (Schwab et al 2010;Cao et al 2016;Xia et al 2017;Qi et al 2018;Chen et al 2019). Following these previous works, we also treat β as a nuisance parameter and marginalize over it using a Gaussian prior with β = 0.18 ± 0.13, based on the well-studied sample of nearby elliptical galaxies.…”

“…1, we also show the redshift distribution of lens and source galaxies of SGL systems. A model-independent method of Gaussian processes (Seikel et al 2012) was applied to reconstruct the dimensionless comoving distance from the ILQSO data straightforwardly, without any parametric assumption regarding cosmological model (Qi et al 2018). However, the fidelity of reconstructed function from most currently available observational data with the Gaussian processes should be further discussed and tested (Zhou & Li 2019).…”

“…So far, several following studies have been carried out with the latest SGL and SNe Ia (Betoule et al 2014) observations at that time (Xia et al 2017;Li et al 2018a). In addition, Qi et al (2018) have used radio quasars as distance indicators (Gurvtis et al 1999;Cao et al 2017a) together with SGL observations to extend the analysis to higher redshift. They obtained that, compared with constraints on the curvature obtained in Räsänen et al (2015), a spatially flat universe is not preferred at higher confidence level.…”