Towards a New Proposal for the Time Delay in Gravitational Lensing

One application of the Cosmological Gravitational Lensing in General Relativity is the measurement of the Hubble constant H 0 using the time delay Δ t between multiple images of lensed quasars. This method has already been applied, obtaining a value of H 0 compatible with that obtained from the SNe 1A, but non-compatible with that obtained studying the anisotropies of the CMB. This difference could be a statistical fluctuation or an indication of new physics beyond the Standard Model of Cosmology, so it desirable to improve the precision of the measurements. At the current technological capabilities it is possible to obtain H 0 to a percent level uncertainty, so a more accurate theoretical model could be necessary in order to increase the precision about the determination of H 0 . The actual formula which relates Δ t with H 0 is approximated; in this paper we expose a proposal to go beyond the previous analysis and, within the context of a new model, we obtain a more precise formula than that present in the literature