Low density regions are less affected by the nonlinear structure formation and baryonic physics. They are ideal places for probing the nature of dark energy, a possible explanation for the cosmic acceleration. Unlike void lensing, which requires identifications of individual voids, we study the stacked lensing signals around the low-density-positions (LDP), defined as places that are devoid of foreground bright galaxies in projection. The method allows a direct comparison with numerical results by drawing correspondence between the bright galaxies with halos. It leads to lensing signals that are significant enough for differentiating several dark energy models. In this work, we use the CFHTLenS catalogue to define LDPs, as well as measuring their background lensing signals. We consider several different definitions of the foreground bright galaxies (redshift range & magnitude cut). Regarding the cosmological model, we run six simulations: the first set of simulations have the same initial conditions, with $rm{w_{de}=-1,-0.5,-0.8,-1.2}$; the second set of simulations include a slightly different $Lambda$CDM model and a w(z) model from cite{2017NatAs...1..627Z}. The lensing results indicate that the models with $rm{w_{de}=-0.5,-0.8}$ are not favored, and the other four models all achieve comparable agreement with the data.
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