Generalized virial theorem in f(R) gravity

TL;DR

This paper extends the virial theorem within f(R) gravity, showing that geometric modifications can explain galaxy cluster mass discrepancies and influence velocity dispersions, offering a new way to test these gravity models observationally.

Contribution

It introduces a generalized virial theorem in f(R) gravity, incorporating geometric terms that account for mass discrepancies in galaxy clusters.

Findings

Geometric mass extends beyond cluster virial radius.

Effective mass from geometric terms explains mass discrepancy.

Velocity dispersion behavior aligns with f(R) gravity predictions.

Abstract

We generalize the virial theorem in f(R) modified gravity using the collisionless Boltzmann equation. We find supplementary geometric terms in the modified Einstein equation providing an effective contribution to the gravitational energy. The total virial mass is proportional to the effective mass associated with the new geometrical term, which may account for the well-known virial theorem mass discrepancy in clusters of galaxies. The model predicts that the geometric mass and its effects extend beyond the virial radius of the clusters. We also consider the behavior of the galaxy cluster velocity dispersion in f(R) models. Thus, the f(R) virial theorem can be an efficient tool in observationally testing the viability of this class of generalized gravity models.