Light deflection angle through velocity profile of galaxies in f(R) model

Vipin Kumar Sharma,Bal Krishna Yadav,Murli Manohar Verma

doi:10.1140/epjc/s10052-021-08908-0

Vipin Kumar Sharma, Bal Krishna Yadav + Show 1 more

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https://doi.org/10.1140/epjc/s10052-021-08908-0

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Abstract

We explore a new realisation of the galactic scale dynamics via gravitational lensing phenomenon in power-law f(R) gravity theory of the type f(R)propto R^{1+delta } with delta<<1 for interpreting the clustered dark matter effects. We utilize the single effective point like potential (Newtonian potential + f(R) background potential) obtained under the weak field limit to study the combined observations of galaxy rotation curve beyond the optical disk size and their lensing profile in f(R) frame work. We calculate the magnitude of light deflection angle with the characteristic length scale (because of Noether symmetry in f(R) theories) appearing in the effective f(R) rotational velocity profile of a typical galaxy with the model parameter delta approx O(10^{-6}) constrained in previous work. For instance, we work with the two nearby controversial galaxies NGC 5533 and NGC 4138 and explore their galactic features by analysing the lensing angle profiles in f(R) background. We also contrast the magnitudes of f(R) lensing angle profiles and the relevant parameters of such galaxies with the generalised pseudo-isothermal galaxy halo model and find consistency.

Highlights

Angle of light due to the Sun provided us with the first unique observational test of general relativity (GR)
The rotation velocity profiles of different galaxies are proved to be the successful tool for the determination of mass distribution, we focus on the observations of rotation curve behaviour beyond the optical disk size for a few galaxies in the modified gravity background and calculate the magnitude of deflection angles by using the f (R) characteristic length scale obtained through the study of outer rotation curves
The gravitational lensing profile is generally used for the mass measurement of astrophysical objects and in this work, we utilized it to test the predictions of modified gravity theory

Summary

Introduction

The most general and the simplest modification in the standard Einstein’s gravity theory is introduced by replacing the Einstein–Hilbert gravity Lagrangian density by a functional form of the Ricci scalar curvature (R) [16,17,18,21,22,23,24,25]. In our previous work [46], we have obtained the modified effective potential in the weak field limit generated by the point-like source of mass M in the f (R) background and explored the flat rotational velocity curves beyond the optical disk in the galaxy dark matter halo region. The values of f (R) galactic length scale free parameter r0 for different galaxies is interpreted in Table 1 via tracing the test mass beyond the outer visible region of galaxies by using Eq (7) We use it in Eq (9) for discussing the plots of the net light deflection angle w.r.t the scaled impact parameter i.e., ξ r0 in f (R) background and to obtain its magnitude.

Generalized pseudo-isothermal dark matter model and lensing profile

Summary and discussions