How to test for possible negative mass of dark matter?

Question

What is the phenomenology of how to test if dark matter has possibly a negative mass (WP negative mass) in particle physics experiments, cosmology or astrophysics?

I lately came across this interesting NASA article,

https://www.nasa.gov/feature/how-dark-matter-could-be-measured-in-the-solar-system

on how to test for dark matter gravitational effects in our own solar system. Most of dark matter is concentrated presumably as a halo around our heliosphere at interstellar space.

image source: https://en.wikipedia.org/wiki/Oort_cloud#/media/File:PIA17046_-_Voyager_1_Goes_Interstellar.jpg

According to the above article a spacecraft sent to interstellar space of our solar system could check for the gravitational effects of dark matter.

But what about Voyager 1? It is already inside interstellar space currently 156AU away. Could the telemetry data of voyager $1$ be used for determining any discrepancy in its velocity from the predicted? Could this be a result of dark matter's gravity?

Specifically, in the case of deceleration observed on the the telemetry data from Voyager 1 that was not predicted, this could indicate that dark matter has a negative mass since it would repel the normal positive matter of Voyager 1 and braking up its velocity. Currently Voyager 1 is travelling trough interstellar space with ~17Km/s.

Would that not be a viable test for possible negative mass of dark matter?

Answer 1

The paper you mention, Farnes 2018, provides an unconventional idea to explain both dark matter and dark energy. However, this idea has quickly been refuted, e.g. by Stepanian 2019 or by Socas-Navarro 2019.

Long-term tracking of the Pioneer probes indeed did result in an observed discrepancy of telemetry data and the expectation from the Post-Newtonian approximation of the Solar System gravity. However, that discrepancy is now understood, thanks to more accurate thermal modeling of the space probe.

Hence, the idea is out, and there is no anomaly measurable even out beyond our Heliospause. That is perfectly expected and consistent with the standard $\Lambda$CDM scenario: a roughly homogeneous mass density from dark matter does not produce an additional force.

That leaves the question whether one might ever use similar probes to find direct evidence for the existence of gravitational pull from dark matter in our solar system. This has recently been studied again. Personally I find the language of that paper to be unnecessarily confusing, my tl;dr of that paper is: nope, not in the foreseeable future.