We investigate the weak lensing effect by line-of-sight structures with a surface mass density of \lesssim 10 ^ { 8 } M _ { \odot } / \textrm { arcsec } ^ { 2 } in QSO-galaxy quadruple lens systems .
Using high-resolution N -body simulations in warm dark matter ( WDM ) models and observed four quadruple lenses that show anomalies in the flux ratios , we obtain constraints on the mass of thermal WDM , m _ { \textrm { WDM } } \geq 1.3 \textrm { keV } ( 95 \% \textrm { CL } ) assuming that the density of the primary lens is described by a singular isothermal ellipsoid ( SIE ) .
The obtained constraint is consistent with those from Lyman- \alpha forests and the number counts of high-redshift galaxies at z > 4 .
Our results show that WDM with a free-streaming comoving wavenumber k _ { \textrm { fs } } \leq 27 h / \textrm { Mpc } is disfavoured as the major component of cosmological density at redshifts 0.5 \lesssim z \lesssim 4 provided that the SIE models describe the gravitational potentials of the primary lenses correctly .