Constraints on the Cosmic Equation of State using Gravitational Lensing Statistics with evolving galaxies

In this paper, observational constraints on the cosmic equation of state of dark energy ($p = w \rho$) have been investigated using gravitational lensing statistics. A likelihood analysis of the lens surveys has been carried out to constrain the cosmological parameters $\Omega_{m}$ and $w$. Constraints on $\Omega_{m}$ and $w$ are obtained in three different models of galaxy evolution: no evolution model (comoving number density of galaxies remain constant), Volmerange and Guiderdoni model and fast merging model. The last two models consider the number evolution of galaxies in addition to the luminosity evolution. The likelihood analysis shows that for the no-evolution case $w \leq -0.04$ and $\Omega_{m}\leq 0.90$ at $1\sigma$ (68% confidence level). Similarly for the Volmerange & Guiderdoni Model the constraints are $w \leq -0.04$ and $\Omega_{m} \leq 0.91$ at $1 \sigma$. In fast merging model the constraint become weaker and it allows almost the entire range of parameters. For the case of constant $\Lambda$ ($w =-1$), all the models permit $\Omega_{m} = 0.3$ with 68% CL which is consistent with the value of $\Omega_{m}$ inferred from various other cosmological observations.