Gravitational focusing of Imperfect Dark Matter

TL;DR

This paper explores how a modified gravity model, resembling imperfect dark matter, causes significant gravitational focusing near the Sun, leading to observable effects on planetary dynamics and constraints from solar system tests.

Contribution

It introduces a specific modification of gravity that mimics imperfect dark matter and analyzes its unique gravitational focusing effects in the Solar system.

Findings

Strong amplification of dark matter density near the Sun

Deviations in the metric due to focusing effects

Constraints on model parameters from PPN bounds

Abstract

Motivated by the projectable Horava--Lifshitz model/mimetic matter scenario, we consider a particular modification of standard gravity, which manifests as an imperfect low pressure fluid. While practically indistinguishable from a collection of non-relativistic weakly interacting particles on cosmological scales, it leaves drastically different signatures in the Solar system. The main effect stems from gravitational focusing of the flow of Imperfect Dark Matter passing near the Sun. This entails strong amplification of Imperfect Dark Matter energy density compared to its average value in the surrounding halo. The enhancement is many orders of magnitude larger than in the case of Cold Dark Matter, provoking deviations of the metric in the second order in the Newtonian potential. Effects of gravitational focusing are prominent enough to substantially affect the planetary dynamics. Using the existing bound on the PPN parameter $\beta_{PPN}$, we deduce a stringent constraint on the unique constant of the model.