Towards a new proposal for the time delay in gravitational lensing

TL;DR

This paper proposes a new theoretical model to improve the precision of Hubble constant measurements via gravitational lensing time delays, addressing discrepancies in current cosmological observations.

Contribution

It introduces a refined formula relating time delay and H_0, surpassing existing approximations in the literature.

Findings

Derived a more accurate formula for time delay in gravitational lensing

Potentially reduces uncertainties in H_0 measurements

Addresses discrepancies between different cosmological data sets

Abstract

One application of the Cosmological Gravitational Lensing in General Relativity is the measurement of the Hubble constant H_0 using the time delay Delta 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 Delta 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.