This study presents results on detecting neutral atomic hydrogen(H I)21 cm absorption in the spectrum of PKS PKS1413+13 at redshift z=0.24670041.The observation was conducted by FAST,with a spectral resolution of10 Hz...This study presents results on detecting neutral atomic hydrogen(H I)21 cm absorption in the spectrum of PKS PKS1413+13 at redshift z=0.24670041.The observation was conducted by FAST,with a spectral resolution of10 Hz,using 10 minutes of observing time.The global spectral profile is examined by modeling the absorption line using a single Gaussian function with a resolution of 10 kHz within a 2 MHz bandwidth.The goal is to determine the rate of the latest cosmic acceleration by directly measuring the redshift evolution of the H I 21 cm absorption line with Hubble flow toward a common background quasar over a decade or longer time span.This will serve as a detectable signal generated by the accelerated expansion of the Universe at redshift z<1,referred to as redshift drift z(5)or the SL effect.The measured H I gas column density in this DLA system is approximately equivalent to the initial observation value,considering uncertainties of the spin temperature of a spiral host galaxy.The high signal-to-noise ratio of 57,obtained at a 10 kHz resolution,strongly supports the feasibility of using the H I 21 cm absorption line in DLA systems to accurately measure the redshift drift rate at a precision level of around 10~(-10)per decade.展开更多
We revisit the epoch of cosmic speed-up characterized by the redshift of transition from a decelerated to an accelerated phase.This redshift is termed the transition redshift(z_(t)).We use the spatially flat and non-f...We revisit the epoch of cosmic speed-up characterized by the redshift of transition from a decelerated to an accelerated phase.This redshift is termed the transition redshift(z_(t)).We use the spatially flat and non-flat variants of the most commonΛCDM and XCDM models to put constraints on the transition redshift along with the other model parameters.The data for this analysis come from the recent and updated Pantheon+supernova(SN)data set and the Hubble parameter measurements obtained from Cosmic Chronometers.We consider both data sets with their respective covariance matrices incorporating all statistical and systematic uncertainties.We observe that using the combined data sets of H(z)and SNe,the best fit value of transition redshift lies in the range 0.61<z_(t)<0.79 for all four dark energy models.Incidentally,we observe a positive curvature for the non-flat models,correlations between several model parameters and a strong degeneracy between the curvature and the equation of state parameter.展开更多
We have investigated late time acceleration for a spatially fiat dust filled Universe in Brans- Dicke theory in the presence of a positive cosmological constant A. Expressions for Hubble＇s constant, luminosity distan...We have investigated late time acceleration for a spatially fiat dust filled Universe in Brans- Dicke theory in the presence of a positive cosmological constant A. Expressions for Hubble＇s constant, luminosity distance and apparent magnitude have been obtained for our model. The theoretical results are compared with observed values of the latest 287 high redshift （0.3 ≤ z ≤1.4） Type Ia supernova data taken from the Union 2.1 compilation to estimate present values of matter and dark energy parame- ters, （Ωm）0 and （ΩA）0. We have also estimated the present value of Hubble＇s constant H0 in light of an updated sample of Hubble parameter measurements including 19 independent data points. The results are found to be in good agreement with recent astrophysical observations. We also calculated various physical parameters such as matter and dark energy densities, present age of the Universe and decelera- tion parameter. The value for Brans-Dicke-coupling constant ω is set to be 40 000 based on accuracy of solar system tests and recent experimental evidence.展开更多
Einstein＇s field equations with variable gravitational and cosmological constants are considered in the presence of perfect fluid for a Robertson-Walker universe by assuming the cosmological term to be proportional t...Einstein＇s field equations with variable gravitational and cosmological constants are considered in the presence of perfect fluid for a Robertson-Walker universe by assuming the cosmological term to be proportional to R-m（R is a scale factor and m is a constant）.A variety of solutions is presented.The physical significance of the cosmological models has also been discussed.展开更多
Einstein＇s field equations with variable gravitational and cosmological constants are considered in the presence of perfect fluid for the Bianchi type-I universe by assuming that the cosmological term is proportional...Einstein＇s field equations with variable gravitational and cosmological constants are considered in the presence of perfect fluid for the Bianchi type-I universe by assuming that the cosmological term is proportional to R-m （R is a scale factor and m is a constant）.A variety of solutions are presented.The physical significance of the respective cosmological models are also discussed.展开更多
In order to explore the properties of cosmic neutrinos, i.e. sum of the neutrino mass （∑mv） and the effective number of neutrino species （Neff）, which affects the Hubble expansion rate H（z） and the power of obs...In order to explore the properties of cosmic neutrinos, i.e. sum of the neutrino mass （∑mv） and the effective number of neutrino species （Neff）, which affects the Hubble expansion rate H（z） and the power of observational Hubble parameter data （OHD） in constraining cosmological parameters under the ACDM model, we utilize OHD to constrain the properties of cosmic neutrinos and apply an accurate H（z） function with ∑ mv, and Neff. First, we simulate new OHD beyond the existing 43 OHD. According to the predictions of measurements of Ho （the current H（z） value）, baryon acoustic oscillations （BAO） peaks, Sandage-Loeb （SL） test and cosmic microwave background （CMB）, we as-sume observational accuracy up to 2% and redshift 0 〈 z ~〈 5. With simulated H（z） data obtained from the fiducial model, we constrain the parameters including ∑ mv, and Neff. When all parameters are set free, ∑mv 〈 0.196eV （95%） and Neff = 2.984 ± 0.826 （68%） are obtained, and when fixing Neff as the standard baseline 3.046, we attain ∑ mv 〈 0.240 eV （95%）. These constrained results are much tighter than the ones obtained by the current OHD, which makes the prospect of OHD in constraining cosmological parameters more promising as its accuracy and quantity grow.展开更多
By adopting the differential age method, we select 17 832 luminous red galaxies from the Sloan Digital Sky Survey Data Release Seven covering redshift 0 〈 z 〈 0.4 to measure the Hubble parameter. Using the full spec...By adopting the differential age method, we select 17 832 luminous red galaxies from the Sloan Digital Sky Survey Data Release Seven covering redshift 0 〈 z 〈 0.4 to measure the Hubble parameter. Using the full spectrum fitting package UZySS, these spectra are reduced with single stellar population models and optimal age information from our selected sample is derived. With the decreasing age-redshift relation, four new observational H（z） data （OHD） points are obtained, which are H（z） = 69.0 ± 19.6 km s^-1 Mpc^-1 at z = 0.07, H（z） = 68.6± 26.2 km s^-1 Mpc^-1 at z = 0.12, H（z）=72.9 ± 29.6 km s^-1 Mpc^-1 at z = 0.2 and H（z）=88.8 ± 36.6 km s^-1 Mpc^-1 at z = 0.28, respectively. Combined with 21 other available OHD data points, the performance of the constraint on both flat and non-flat ACDM models is presented.展开更多
We use the distance sum rule method to constrain the spatial curvature of the Universe with a large sample of 161strong gravitational lensing systems,whose distances are calibrated from the Pantheon compilation of typ...We use the distance sum rule method to constrain the spatial curvature of the Universe with a large sample of 161strong gravitational lensing systems,whose distances are calibrated from the Pantheon compilation of typeⅠa supernovae using deep learning.To investigate the possible influence of mass model of the lens galaxy on constraining the curvature parameterΩ_(k),we consider three different lens models.Results show that a flat Universe is supported in the singular isothermal sphere(SIS)model with the parameterΩ_(k)=0.049_(-0.125)^(+0.147).While in the power-law(PL)model,a closed Universe is preferred at the~3σconfidence level,with the parameterΩ_(k)=-0.245_(-0.071)^(+0.075).In the extended PL model,the 95%confidence level upper limit ofΩ_(k)is<0.011.As for the parameters of the lens models,constraints on the three models indicate that the mass profile of the lens galaxy could not be simply described by the standard SIS model.展开更多
An action of general form is proposed for a Universe containing matter, radiation and dark energy. The latter is interpreted as a tachyon field non-minimally coupled to the scalar curvature. The Palatini approach is u...An action of general form is proposed for a Universe containing matter, radiation and dark energy. The latter is interpreted as a tachyon field non-minimally coupled to the scalar curvature. The Palatini approach is used when varying the action so the connection is given by a more generic form. Both the self-interaction potential and the non-minimally coupling function are obtained by constraining the system to present invariability under global point transformation of the fields （Noether Symmetry）. The only possible solution is shown to be that of minimal coupling and constant potential （Chaplygin gas）. The behavior of the dynamical properties of the system is compared to recent observational data, which infers that the tachyon field must indeed be dynamical.展开更多
We study a known class of scalar dark energy models in which the potential has an exponential term and the current accelerating era is transient. We find that, although a decelerating era will return in the future, wh...We study a known class of scalar dark energy models in which the potential has an exponential term and the current accelerating era is transient. We find that, although a decelerating era will return in the future, when extrapolating the model back to earlier stages （z ≥ 4）, scalar dark energy becomes dominant over matter. So these models do not have the desired tracking behavior, and the predicted transient period of acceleration cannot be adopted into the standard scenario of the Big Bang cosmology. When couplings between the scalar field and matter are introduced, the models still have the same problem; only the time when deceleration returns will be varied. To achieve re-deceleration, one has to turn to alternative models that are consistent with the standard Big Bang scenario.展开更多
The power spectrum of the two-degree Field Galaxy Redshift Survey （2dFGRS） sample is estimated with the discrete wavelet transform （DWT） method. The DWT power spectra within 0.035 〈 k 〈 2.2 h Mpc^-1 are measured...The power spectrum of the two-degree Field Galaxy Redshift Survey （2dFGRS） sample is estimated with the discrete wavelet transform （DWT） method. The DWT power spectra within 0.035 〈 k 〈 2.2 h Mpc^-1 are measured for three volume-limited samples defined in consecutive absolute magnitude bins - 19 - - 18, - 20 - - 19 and - 21 - - 20. We show that the DWT power spectrum can effectively distinguish ACDM models of σ8 = 0.84 and σ8 = 0.74. We adopt maximum likelihood method to perform three-parameter fitting of the bias parameter b, pairwise velocity dispersion σpv and redshift distortion parameterβ = Ωm^0.6/b to the measured DWT power spectrum. The fitting results state that in a σ8 = 0.84 universe the best-fit values of Ωm given by the three samples are mutually consistent within the range 0.28 - 0.36, and the best fitted values of Opv are 398-27^＋35, 475-29^37 and 550 ± 20 km s^-1 for the three samples, respectively. In the model of σ8 = 0.74, our three samples give very different values of Ωm. We repeated the fitting using the empirical formula of redshift distortion. The result of the model of low σ8 is still poor, especially, one of the best-fit values of σpv is as large as 10^3 km s^-1. We also repeated our fitting by incorporating a scale-dependent galaxy bias. This gave a slightly lower value of Ωm. Differences between the models of σ8 = 0.84 and σ8 = 0.74 still exist in the fitting results. The power spectrum of 2dFGRS seems to disfavor models with low amplitude of density fluctuations if the bias parameter is assumed to be scale independent. For the fitting value of Ωm to be consistent with that given by WMAP3, strong scale dependence of the bias parameters is needed.展开更多
We explore the problems of degeneracy and discreteness in the standard cosmological model（ΛCDM）. We use the Observational Hubble Data（OHD） and the type Ia supernovae（SNe Ia） data to study this issue. In order t...We explore the problems of degeneracy and discreteness in the standard cosmological model（ΛCDM）. We use the Observational Hubble Data（OHD） and the type Ia supernovae（SNe Ia） data to study this issue. In order to describe the discreteness in fitting of data, we define a factor G to test the influence from each single data point and analyze the goodness of G. Our results indicate that a higher absolute value of G shows a better capability of distinguishing models, which means the parameters are restricted into smaller confidence intervals with a larger figure of merit evaluation. Consequently, we claim that the factor G is an effective way of model differentiation when using different models to fit the observational data.展开更多
We study the statistics of large-separation multiply-imaged quasars lensed by clusters of galaxies. In particular, we examine how the observed brightest cluster galaxies （BCGs） affect the predicted numbers of wide-s...We study the statistics of large-separation multiply-imaged quasars lensed by clusters of galaxies. In particular, we examine how the observed brightest cluster galaxies （BCGs） affect the predicted numbers of wide-separation lenses. We model the lens as an NFW-profiled dark matter halo with a truncated singular isothermal sphere to represent the BCG in its center. We mainly make predictions for the Sloan Digital Sky Survey Quasar Lens Search （SQLS） sample from the Data Release 5 （DRS） in two standard ACDM cosmological models： a model with matter density ΩM = 0.3 and δ8 = 0.9, as is usually adopted in the literature （ACDM1）, and a model suggested by the WMAP seven-year （WMAPT） data with ΩM = 0.266 and δ8 = 0.801. We also study the lensing properties for the WMAP3 cosmology in order to compare with the previous work. We find that BCGs in the centers of clusters significantly enhance the lensing efficiency by a factor of 2 - 3 compared with that of NFW-profiled pure dark matter halos. In addition, the dependence of mass ratios of BCGs to their host halos on the host halo masses reduces the lensing rate by - 20% from assuming a constant ratio as in previous studies, but considering the evolution of this ratio with redshift out to z - 1 would reduce it by - 3%. Moreover, we predict that the numbers of lensed quasars with image separations larger than 10″ in the statistical sample of SQLS from DR5 are 1.22 and 0.47, respectively for ACDM1 and WMAP7 and 0.73 and 0.33 for separations between 10″ and 20″, which are consistent with the only observed cluster lens with such a large separation in the complete SQLS sample.展开更多
基金supported by the National SKA Program of China(2022SKA0110202)the National Natural Science Foundation of China(grants No.11929301)。
文摘This study presents results on detecting neutral atomic hydrogen(H I)21 cm absorption in the spectrum of PKS PKS1413+13 at redshift z=0.24670041.The observation was conducted by FAST,with a spectral resolution of10 Hz,using 10 minutes of observing time.The global spectral profile is examined by modeling the absorption line using a single Gaussian function with a resolution of 10 kHz within a 2 MHz bandwidth.The goal is to determine the rate of the latest cosmic acceleration by directly measuring the redshift evolution of the H I 21 cm absorption line with Hubble flow toward a common background quasar over a decade or longer time span.This will serve as a detectable signal generated by the accelerated expansion of the Universe at redshift z<1,referred to as redshift drift z(5)or the SL effect.The measured H I gas column density in this DLA system is approximately equivalent to the initial observation value,considering uncertainties of the spin temperature of a spiral host galaxy.The high signal-to-noise ratio of 57,obtained at a 10 kHz resolution,strongly supports the feasibility of using the H I 21 cm absorption line in DLA systems to accurately measure the redshift drift rate at a precision level of around 10~(-10)per decade.
文摘We revisit the epoch of cosmic speed-up characterized by the redshift of transition from a decelerated to an accelerated phase.This redshift is termed the transition redshift(z_(t)).We use the spatially flat and non-flat variants of the most commonΛCDM and XCDM models to put constraints on the transition redshift along with the other model parameters.The data for this analysis come from the recent and updated Pantheon+supernova(SN)data set and the Hubble parameter measurements obtained from Cosmic Chronometers.We consider both data sets with their respective covariance matrices incorporating all statistical and systematic uncertainties.We observe that using the combined data sets of H(z)and SNe,the best fit value of transition redshift lies in the range 0.61<z_(t)<0.79 for all four dark energy models.Incidentally,we observe a positive curvature for the non-flat models,correlations between several model parameters and a strong degeneracy between the curvature and the equation of state parameter.
基金supported by the CGCOST Research Project 789/CGCOST/MRP/14
文摘We have investigated late time acceleration for a spatially fiat dust filled Universe in Brans- Dicke theory in the presence of a positive cosmological constant A. Expressions for Hubble＇s constant, luminosity distance and apparent magnitude have been obtained for our model. The theoretical results are compared with observed values of the latest 287 high redshift （0.3 ≤ z ≤1.4） Type Ia supernova data taken from the Union 2.1 compilation to estimate present values of matter and dark energy parame- ters, （Ωm）0 and （ΩA）0. We have also estimated the present value of Hubble＇s constant H0 in light of an updated sample of Hubble parameter measurements including 19 independent data points. The results are found to be in good agreement with recent astrophysical observations. We also calculated various physical parameters such as matter and dark energy densities, present age of the Universe and decelera- tion parameter. The value for Brans-Dicke-coupling constant ω is set to be 40 000 based on accuracy of solar system tests and recent experimental evidence.
文摘Einstein＇s field equations with variable gravitational and cosmological constants are considered in the presence of perfect fluid for a Robertson-Walker universe by assuming the cosmological term to be proportional to R-m（R is a scale factor and m is a constant）.A variety of solutions is presented.The physical significance of the cosmological models has also been discussed.
文摘Einstein＇s field equations with variable gravitational and cosmological constants are considered in the presence of perfect fluid for the Bianchi type-I universe by assuming that the cosmological term is proportional to R-m （R is a scale factor and m is a constant）.A variety of solutions are presented.The physical significance of the respective cosmological models are also discussed.
基金supported by the National Key R&D Program of China(2017YFA0402600)the National Natural Science Foundation of China(Grant Nos.11573006 and 11528306)+1 种基金the Fundamental Research Funds for the Central Universitiesthe Special Program for Applied Research on Super Computation of the NSFC-Guangdong Joint Fund(the second phase)
文摘In order to explore the properties of cosmic neutrinos, i.e. sum of the neutrino mass （∑mv） and the effective number of neutrino species （Neff）, which affects the Hubble expansion rate H（z） and the power of observational Hubble parameter data （OHD） in constraining cosmological parameters under the ACDM model, we utilize OHD to constrain the properties of cosmic neutrinos and apply an accurate H（z） function with ∑ mv, and Neff. First, we simulate new OHD beyond the existing 43 OHD. According to the predictions of measurements of Ho （the current H（z） value）, baryon acoustic oscillations （BAO） peaks, Sandage-Loeb （SL） test and cosmic microwave background （CMB）, we as-sume observational accuracy up to 2% and redshift 0 〈 z ~〈 5. With simulated H（z） data obtained from the fiducial model, we constrain the parameters including ∑ mv, and Neff. When all parameters are set free, ∑mv 〈 0.196eV （95%） and Neff = 2.984 ± 0.826 （68%） are obtained, and when fixing Neff as the standard baseline 3.046, we attain ∑ mv 〈 0.240 eV （95%）. These constrained results are much tighter than the ones obtained by the current OHD, which makes the prospect of OHD in constraining cosmological parameters more promising as its accuracy and quantity grow.
基金supported by the National Natural Science Foundation of China
文摘By adopting the differential age method, we select 17 832 luminous red galaxies from the Sloan Digital Sky Survey Data Release Seven covering redshift 0 〈 z 〈 0.4 to measure the Hubble parameter. Using the full spectrum fitting package UZySS, these spectra are reduced with single stellar population models and optimal age information from our selected sample is derived. With the decreasing age-redshift relation, four new observational H（z） data （OHD） points are obtained, which are H（z） = 69.0 ± 19.6 km s^-1 Mpc^-1 at z = 0.07, H（z） = 68.6± 26.2 km s^-1 Mpc^-1 at z = 0.12, H（z）=72.9 ± 29.6 km s^-1 Mpc^-1 at z = 0.2 and H（z）=88.8 ± 36.6 km s^-1 Mpc^-1 at z = 0.28, respectively. Combined with 21 other available OHD data points, the performance of the constraint on both flat and non-flat ACDM models is presented.
文摘We use the distance sum rule method to constrain the spatial curvature of the Universe with a large sample of 161strong gravitational lensing systems,whose distances are calibrated from the Pantheon compilation of typeⅠa supernovae using deep learning.To investigate the possible influence of mass model of the lens galaxy on constraining the curvature parameterΩ_(k),we consider three different lens models.Results show that a flat Universe is supported in the singular isothermal sphere(SIS)model with the parameterΩ_(k)=0.049_(-0.125)^(+0.147).While in the power-law(PL)model,a closed Universe is preferred at the~3σconfidence level,with the parameterΩ_(k)=-0.245_(-0.071)^(+0.075).In the extended PL model,the 95%confidence level upper limit ofΩ_(k)is<0.011.As for the parameters of the lens models,constraints on the three models indicate that the mass profile of the lens galaxy could not be simply described by the standard SIS model.
基金CNPq for the financial support that allowed this work to be done
文摘An action of general form is proposed for a Universe containing matter, radiation and dark energy. The latter is interpreted as a tachyon field non-minimally coupled to the scalar curvature. The Palatini approach is used when varying the action so the connection is given by a more generic form. Both the self-interaction potential and the non-minimally coupling function are obtained by constraining the system to present invariability under global point transformation of the fields （Noether Symmetry）. The only possible solution is shown to be that of minimal coupling and constant potential （Chaplygin gas）. The behavior of the dynamical properties of the system is compared to recent observational data, which infers that the tachyon field must indeed be dynamical.
基金supported by the National Natural Science Foundation of China (GrantNo. 10773009), SRFDP and CAS
文摘We study a known class of scalar dark energy models in which the potential has an exponential term and the current accelerating era is transient. We find that, although a decelerating era will return in the future, when extrapolating the model back to earlier stages （z ≥ 4）, scalar dark energy becomes dominant over matter. So these models do not have the desired tracking behavior, and the predicted transient period of acceleration cannot be adopted into the standard scenario of the Big Bang cosmology. When couplings between the scalar field and matter are introduced, the models still have the same problem; only the time when deceleration returns will be varied. To achieve re-deceleration, one has to turn to alternative models that are consistent with the standard Big Bang scenario.
基金the National Natural Science Foundation of China
文摘The power spectrum of the two-degree Field Galaxy Redshift Survey （2dFGRS） sample is estimated with the discrete wavelet transform （DWT） method. The DWT power spectra within 0.035 〈 k 〈 2.2 h Mpc^-1 are measured for three volume-limited samples defined in consecutive absolute magnitude bins - 19 - - 18, - 20 - - 19 and - 21 - - 20. We show that the DWT power spectrum can effectively distinguish ACDM models of σ8 = 0.84 and σ8 = 0.74. We adopt maximum likelihood method to perform three-parameter fitting of the bias parameter b, pairwise velocity dispersion σpv and redshift distortion parameterβ = Ωm^0.6/b to the measured DWT power spectrum. The fitting results state that in a σ8 = 0.84 universe the best-fit values of Ωm given by the three samples are mutually consistent within the range 0.28 - 0.36, and the best fitted values of Opv are 398-27^＋35, 475-29^37 and 550 ± 20 km s^-1 for the three samples, respectively. In the model of σ8 = 0.74, our three samples give very different values of Ωm. We repeated the fitting using the empirical formula of redshift distortion. The result of the model of low σ8 is still poor, especially, one of the best-fit values of σpv is as large as 10^3 km s^-1. We also repeated our fitting by incorporating a scale-dependent galaxy bias. This gave a slightly lower value of Ωm. Differences between the models of σ8 = 0.84 and σ8 = 0.74 still exist in the fitting results. The power spectrum of 2dFGRS seems to disfavor models with low amplitude of density fluctuations if the bias parameter is assumed to be scale independent. For the fitting value of Ωm to be consistent with that given by WMAP3, strong scale dependence of the bias parameters is needed.
基金supported by the National Natural Science Foundation of China(Grant No.11173006)the National Basic Research Program of China(project 973,No.2012CB821804)
文摘We explore the problems of degeneracy and discreteness in the standard cosmological model（ΛCDM）. We use the Observational Hubble Data（OHD） and the type Ia supernovae（SNe Ia） data to study this issue. In order to describe the discreteness in fitting of data, we define a factor G to test the influence from each single data point and analyze the goodness of G. Our results indicate that a higher absolute value of G shows a better capability of distinguishing models, which means the parameters are restricted into smaller confidence intervals with a larger figure of merit evaluation. Consequently, we claim that the factor G is an effective way of model differentiation when using different models to fit the observational data.
基金supported by the National Natural Science Foundation of China(Grant No. 11073023)the National Basic Research Program of China (973 ProgramGrant No.2009CB24901)
文摘We study the statistics of large-separation multiply-imaged quasars lensed by clusters of galaxies. In particular, we examine how the observed brightest cluster galaxies （BCGs） affect the predicted numbers of wide-separation lenses. We model the lens as an NFW-profiled dark matter halo with a truncated singular isothermal sphere to represent the BCG in its center. We mainly make predictions for the Sloan Digital Sky Survey Quasar Lens Search （SQLS） sample from the Data Release 5 （DRS） in two standard ACDM cosmological models： a model with matter density ΩM = 0.3 and δ8 = 0.9, as is usually adopted in the literature （ACDM1）, and a model suggested by the WMAP seven-year （WMAPT） data with ΩM = 0.266 and δ8 = 0.801. We also study the lensing properties for the WMAP3 cosmology in order to compare with the previous work. We find that BCGs in the centers of clusters significantly enhance the lensing efficiency by a factor of 2 - 3 compared with that of NFW-profiled pure dark matter halos. In addition, the dependence of mass ratios of BCGs to their host halos on the host halo masses reduces the lensing rate by - 20% from assuming a constant ratio as in previous studies, but considering the evolution of this ratio with redshift out to z - 1 would reduce it by - 3%. Moreover, we predict that the numbers of lensed quasars with image separations larger than 10″ in the statistical sample of SQLS from DR5 are 1.22 and 0.47, respectively for ACDM1 and WMAP7 and 0.73 and 0.33 for separations between 10″ and 20″, which are consistent with the only observed cluster lens with such a large separation in the complete SQLS sample.
