Gravitational Lensing in the standard ΛCDM Cosmology

Abstract

Gravitational lensing is one of the powerful methods for astrophysical investigations where General Relativity (GR) is being applied. But, the appropriate parameters incorporated in GR are still at debate among the scientific communities. Especially, the incorporation of cosmological constant Λ was controversial from its origin to its significance. However, recent progress indicates that cosmological models require a form of dark matter-energy sector that will behave in an old enough universe with energy content in the form of Λ. So, here we worked out the effect of Λ in gravitational lensing where an effective refractive index in vacuum is considered to accommodate it. Thus GR equations were being used to derive lensing equation in the presence of Λ with simplifying boundary conditions. The adopted method is so simple but agrees with the one derived from complex and more boundary value considerations. Moreover, its significant at cosmological scale goes up to 2%, that cannot be neglected.