On the other hand, observational data are used to test these models. Among the most frequently used are the cosmic microwave background radiation (CMB; Planck Collaboration XIII 2016; Aghanim et al. 2018), baryonic acoustic oscillations (BAO; Eisenstein et al. 2005; Blake et al. 2012; Alam et al. 2017; Bautista et al. 2017), Type Ia supernovae (SNe Ia; Scolnic et al. 2018), and observational Hubble data (OHD; Jimenez & Loeb 2002; Moresco et al. 2016; Magaña et al. 2018). Consistency in the cosmological parameters among different techniques, rather than more accurate measurements, is desirable to better understand the nature of DE. In the last years, several efforts have been made by the community to include gravitational lens systems in the study of the Universe’s evolution. Some of the pioneers are Futamase & Yoshida (2001) and Biesiada (2006), who used only one strong-lens system to study some of the most popular cosmological models. Grillo, Lombardi & Bertin (2008) introduced a methodology to estimate cosmological parameters using strong-lensing systems (SLS; see also Jullo et al. 2010; Magaña et al. 2015, 2018). They apply the relation between the Einstein radius and the central stellar velocity dispersion, assuming an isothermal profile for the total density distribution of the lens (elliptical) galaxy. Their simulations found that the method is accurate enough to obtain information about the underlying cosmology. They concluded that the stellar velocity dispersion and velocity dispersion of the isothermal lens model are very similar in the w cold dark matter (wCDM) model. Biesiada, Piórkowska & Malec (2010) used the same procedure comparing a distance ratio, Dobs, constructed from SLS observations such as the Einstein radius and spectroscopic velocity dispersion of the lens galaxy, with a theoretical counterpart, Dth. By using a sample containing 20 SLS, they demonstrated that this technique is useful to provide insights into DE. Cao et al. (2012) updated the sample to 80 systems and proposed a modification that takes into account deviations from sphericity, i.e. from the singular isothermal sphere (SIS). Later on, Cao et al. (2015) considered lens profile deviations due to the redshift evolution of elliptical galaxies by using spherically symmetric power-law mass distributions for the lenses and also increased the compilation up to 118 points. They also explore the consequences of using aperture-corrected velocity dispersions on the parameter estimations. Some authors have pointed out the need for a sufficiently large sample to test DE models with higher precision (Yennapureddy & Melia 2018). For instance, Melia, Wei & Wu (2015) have emphasized that a sample of ∼200 SLS can discern the Rh = ct model from the standard one. Qi et al. (2018) simulated strong lensing data to constrain the curvature of the Universe and found that, by increasing the sample (16000 lenses) and combining with compact radio quasars, it could be constrained with an accuracy of ∼10−3. Recently, Leaf & Melia (2018) have revisited this cosmological tool with the largest sample of SLS (158) until now, including 40 new systems presented by Shu et al. (2017). The authors proposed a new approach to improve this technique by introducing in the observational distance ratio error (δDobs), a parameter σx to take into account the SIE scatter and any other source of errors in the measurements. In their analysis, they excluded 29 SLS that are outside the region 0  Dobs  1, and the system SL2SJ085019−034710 (Sonnenfeld et al. 2013b), which seems to be an extreme outlier for their models. Their results show that a $\sigma _x = 12.2{{\ \rm per\ cent}}$ provides more statistically significative cosmological constraints. Finally, Chen, Li & Shu (2018) used 157 SLS to analyse the Lambda cold dark matter (ΛCDM) model. They considered a lens mass distribution ρ(r) = ρ0r−γ and three possibilities for the γ parameter: a constant value, a dependence with the lens redshift (zl), and a dependence with both the surface mass density and the lens redshift. They concluded that although Ω0m, used as the only free parameter in ΛCDM scenario, is very sensitive to the lens mass model, it provides weak constraints that are also in tension with Planck measurements.
Citation: Magaña et al. 2015
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