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A New Explanation of Dark Matter-Plasma Shift in Bullet Cluster by Modification of Gravity

EasyChair Preprint no. 8731

5 pagesDate: August 29, 2022

Abstract

The explanation of the cluster dynamics in the Einstein's theory of gravity via gravitational lensing observation of the Bullet Cluster (1E0657-558) at a redshift, z~ 0.296 presumably invokes the evidence for dark matter. This is revealed by the Hubble Space Telescope (HST) / Advanced Camera Survey (ACS) images of the cluster cores of the stellar component and the fluid-like X-ray emitting plasma (the most dominant baryonic component) by the Chandra Space Satellite. It is observed from such images that the k-map (a measure of the curvature or convergence of spacetime through gravitational lensing) and the $\Sigma$-map (a measure of the surface mass density of the hot intercluster medium (plasma) through King $\beta$ model have the different peaks. However, the peak value of the k-map does not trace the dominant component (plasma) but rather traces the galaxies (stellar component). In the present work, we attempt to explain this cluster scale anomaly without the need of any dark matter of the standard form but by modifying the Einstein's law of gravity in a way that under the weak field limit the theory satisfies the galactic dynamics as well as the local gravity constraints via a chameleon mechanism. We work with the modified Einstein - Hilbert action using $f(R)=R^{1+\delta}/R_c^{\delta}$, $\delta<<$1 shows the deviation from Einstein's gravity theory. We obtain the gravitational lensing angle formula in the modified gravity background and use it to calculate the gravitational lensing potential and convergence or the scaled surface mass density, k ( as $\Sigma$ / $\Sigma_{(critical)}$) for the Bullet Cluster. We claim that this modified convergence may be held responsible for the observed shifting of the peak of the gravitational potential from the dominant plasma component of the Cluster.

Keyphrases: dark matter, Lensing angle, modified gravity

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