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

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 $$f(R)\propto R^{1+\delta }$$ f ( R ) ∝ R 1 + δ with $$\delta<<1$$ δ < < 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 $$\delta \approx O(10^{-6})$$ δ ≈ 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.

Unified f(R) gravity at local scales

“…3, 4) to choose the narrow values of δ( 1) for conformal equivalence. The small (about 10 −6 ) value of δ is also recently confirmed from our study of galactic dynamics [50,51].…”

“…We investigate the constraints corresponding to different geodesics (null and non-null) along with their conformal analogue at the galactic and planetary scales under an idealistic consideration with the f (R) modified potential explored in [57][58][59]. Moreover, our recent combined analysis of light deflection profiles via rotation curves for typical spiral massive galaxies may, in principle, also distinguish the present f (R) model from other profiles in standard dark matter model of galaxy (say Pseudo-isothermal model) in terms of lensing angle [51]. With such motivation along with work of several authors such as [55], we look for δ as a distinguishing parameter for the phenomenological investigation of constraints through a study of different geodesics with the conformal analogue.…”

“…Along this direction, as motivated by the dynamical modelling of massive test masses in f (R) gravity model by B öhmer et al [55] and also by our recently investigated power-law f (R) model at low redshifts [49][50][51] and by others [56][57][58][59] for the clustered dark matter explanation, we further analyze here the strict phenomenological constraints on the model parameter δ in R → R 1+δ . We investigate the constraints corresponding to different geodesics (null and non-null) along with their conformal analogue at the galactic and planetary scales under an idealistic consideration with the f (R) modified potential explored in [57][58][59].…”

“…On one hand, it can address the dark sector (dark matter and dark energy) with the different degrees of freedom, [32] and on the other, it can precisely address the deviation from the existing gravity theory i.e. Einstein's GR theory with some new dynamical features, which at present is very exciting issue in literature [47][48][49][50][51][52][53]. Such alternate gravity theory may also pave a possible approach to study the unified theory of dark matter and dark energy [54].…”

Effect of the Modified Gravity on the Large-scale Structure Formation

“…One of the most popular models in f (R) gravity (Amendola et al 2007;Appleby & Battye 2007;Hu & Sawicki 2007;Percival et al 2007;Starobinsky 2007;Tsujikawa 2008) is the Dvali-Gabadadze-Porrati (DGP) brane-world model (Dvali et al 2000), beyond the ΛCDM model. In this paper we have used the power-law models (Capozziello et al 2003;Carloni et al 2005;Jaime 2013;Motohashi 2015;Sharma & Verma 2022a, 2022bSharma et al 2020Sharma et al , 2021Yadav & Verma 2019), the Starobinsky model (Starobinsky 1998), and the ΛCDM model (Sahni & Starobinsky 2000;Padmanabhan 2003) to study the matter density perturbations and compare their results with observations (Cole et al 2005) in the linear regime.…”