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

Abstract

Model-independent measurements for the cosmic spatial curvature, which is related to the nature of cosmic space-time geometry, plays an important role in cosmology. On the basis of the Distance Sum Rule in the Friedmann-Lemaître-Robertson-Walker metric, (distance ratio) measurements of strong gravitational lensing (SGL) systems together with distances from type Ia supernovae observations have been proposed to directly estimate the spatial curvature without any assumptions for the theories of gravity and contents of the universe. However, previous studies indicated that a spatially closed universe was strongly preferred. In this paper, we re-estimate the cosmic curvature with the latest SGL data which includes 163 well-measured systems. In addition, possible factors, e.g. combination of SGL data from different surveys and stellar mass of the lens galaxy, which might affect estimations for the spatial curvature, are considered in our analysis. We find that, except the case where only SGL systems from the Sloan Lens ACS Survey are considered, a spatially flat universe is consistently favored at very high confidence level by the latest observations. It is suggested that the increasing number of well-measured strong lensing events might significantly reduce the bias of estimation for the cosmic curvature.

Model-independent constraints on cosmic curvature: implication from the future space gravitational-wave antenna DECIGO

“…The precision of this estimate is comparable to the recent analysis of Cao et al [10], which represented the precision of ΔΩ k ∼ 10 −2 with 250 well-observed radio quasars. Such conclusion is also well consistent with the cosmic curvature derived from the strong lensing and supernova distance measurements in the framework of another model-independent test based on the distance sum rule [15].…”

“…In other words the expected precision is ΔΩ k = 10 −2 with the DECIGO+CC and ΔΩ k = 10 −1 with the ET+CC. Compared to the latest model-independent estimations of the spatial curvature using the distance sum rule method [15], our results suggest a considerable improvement in precision when the future GW observatories provide rich statistics of D L (z) measurements. In order to surpass the limitations of small CC sample we reconstructed H (z) function using GP technique and used it together with reconstructed D L (z) and D L (z) to investigate Ω k (z).…”

“…Such methodology was then applied to test the validity to FLRW metric, based on the galactic-scale lensing systems where strongly lensed gravitational waves and their electromagnetic counterparts can be simultaneously detected [10]. More recently, Qi et al [14], Zhou et al [15] extended the cosmic curvature analysis to higher redshift, using the latest data sets of strong lensing systems [16,17] combined with intermediate-luminosity quasars calibrated as standard rulers [18]. Another straightforward method to constrain the cosmic curvature has been proposed by Clarkson et al [6], using the expansion rate measurements H(z) and the transverse comoving distances D(z).…”

Cosmology-independent Estimate of the Hubble Constant and Spatial Curvature Using Time-delay Lenses and Quasars

“…There are always differences between the lensing redshifts and the nearest quasars. This issue can be overcame by reconstructing a continuous distance function that best approximates the discrete observed data using a polynomial fit (Räsänen et al 2015;Liao et al 2017;Li et al 2018a;Collett et al 2019;Liao 2019;Zhou & Li 2020). In our analysis, we construct the dimensionless distance function d(z) in a cosmology independent way by fitting a third-order polynomial with initial conditions d(0) = 0 and d ′ (0) = 1, to the quasar data.…”

“…Furthermore, the comparision of the inferred values of the cosmic curvature from two or more lens-source pairs provides a consistency test of the FLRW metric (Räsänen et al 2015). Based on the sum rule of distances along null geodesics of the FLRW metric, modelindependent determinations of the spatial curvature have been implemented by combining strong gravitational lensing systems with other distance indicators, including SNe Ia (Räsänen et al 2015;Liao et al 2017Liao et al , 2019Liao et al , 2020Xia et al 2017;Denissenya et al 2018;Li et al 2018a;Collett et al 2019;Zhou & Li 2020), gravitational waves (GWs; Liao 2019), and compact radio sources (Qi et al 2019b). Such model-independent curvature determinations have also been proposed using future time delay measurements of strongly lensed transients (such as fast radio bursts, GWs, and SNe) and luminosity distances of SNe Ia (Li et al 2018b(Li et al , 2019Qi et al 2019a).…”