A Relativistic Tensorial Model for Fractional Interaction between Dark Matter and Gravity

TL;DR

This paper develops a relativistic tensorial model for fractional interactions between dark matter and gravity, extending previous scalar models, and tests its predictions against galaxy cluster lensing data, showing good agreement.

Contribution

It introduces a non-local, relativistic tensorial extension of fractional gravity models, incorporating Ricci tensor couplings and deriving field equations for dark matter interactions.

Findings

The model reduces to general relativity in the weak field limit.

Predictions match observed galaxy cluster lensing profiles.

The framework accommodates pressureless dark matter with non-local effects.

Abstract

In a series of recent papers it was shown that several aspects of Dark Matter (DM) phenomenology, such as the velocity profiles of individual dwarfs and spiral galaxies, the scaling relations observed in the latter, and the pressure and density profiles of galaxy clusters, can be explained by assuming the DM component in virialized halos to feel a non-local fractional interaction mediated by gravity. Motivated by the remarkable success of this model, in a recent work we have looked for a general relativistic extension, proposing a theory, dubbed Relativistic Scalar Fractional Gravity or RSFG, in which the trace of the DM stress-energy tensor couples to the scalar curvature via a non-local operator constructed with a fractional power of the d'Alembertian. In this work we construct an extension of that model in which also a non-local coupling between the Ricci tensor and the DM stress energy tensor is present. In the action we encode the normalization between these scalar and tensorial term into two operators $F_0(\Box)$ and $F_2(\Box)$, and we derive the general field equations. We then take the weak field limit of the latter, showing that they reduce to general relativity sourced by an effective stress energy tensor, featuring a non local isotropic pressure and anisotropic stress, even if one starts with the assumption of a pressureless DM fluid. Finally, after having worked out the lensing theory in our setup, we test particularly interesting realizations of our framework against the measured convergence profiles of the individual and stacked clusters of the CLASH sample, finding remarkable consistency with the data.