**Authors: **Gabriel Chardin, Yohan Dubois, Giovanni Manfredi, Bruce Miller and Clément Stahl

**First Author’s Institution: **Université de Paris, CNRS, Astroparticule et Cosmologie, Paris, France

**Status: **Submitted to arXiv (open access)

In the 1930s, observations of the Coma cluster showed that the peculiar velocities of its galaxies are way too large compared to what they should be (based on the visible mass). Several decades later, Vera Rubin and Albert Bosma found that rotation curves – a measure of the rotational velocity of a galaxy as a function of the distance from its centre – remain flat instead of decreasing, seemingly in defiance of Newton’s law of universal gravitation. In the years since, solutions to these problems have largely fallen into two competing theories. The first hypothesis is the presence of a large amount of invisible matter that provides the necessary mass to account for the otherwise anomalous dynamics of galaxies. This dark matter is a core component of the current standard cosmological model: Lambda cold dark matter (LCDM). Although LCDM is highly successful, it is not without its problems. Dark matter itself is yet to be directly observed, and the recent discovery of dark-matter deficient galaxies has challenged the assumption that dark matter comprises the overwhelming bulk of a galaxy’s mass.

### The Matter We Cannot See

There is a second hypothesis to explain rotation curves; one that does not require dark matter at all. Instead, this theory modifies the laws of gravity itself. Modified Newtonian Dynamics (or MOND) adds a new acceleration parameter to Newton’s law of gravitation. This modification is largely based on observational evidence, and while MOND has been successful at reproducing galaxy scaling relations such as the Tully-Fischer relation, there is little theoretical justification for adding an extra acceleration parameter, although it is known that such a parameter could be warranted were gravity polarised. The authors of this paper consider an alternate cosmological model – the Dirac-Milne universe – and show that under this model, there is a physical basis for an acceleration parameter through the polarisation of matter and antimatter!

### The Isola and The Pale

The Dirac-Milne universe, proposed in 2012, is a radical departure from LCDM. Instead of populating the cosmos with hypothetical particles, a Dirac-Milne universe is a symmetric matter-antimatter universe, where matter and antimatter repel each other. Antimatter can be thought of as having a “negative” mass. In this model, galaxies – made of ordinary matter – are compact objects that lie in the centre of a “depletion zone”, a spherical region that is devoid of any matter or antimatter. The depletion zone, which has a radius given by the depletion radius r_{d}, is then surrounded by an “antimatter cloud” with a roughly constant density. The depletion zone thus acts as a barrier, preventing the matter and antimatter from coming into contact and self-annihilating. Figure 1 shows what this looks like in the author’s large-scale simulation.

### An Altered Curve

One can calculate the expected rotation curves, i.e., the rotational velocity as a function of the distance to the galaxy centre. The velocity reaches a minimum at approximately 0.8 times the depletion radius, before rising slightly. This translates into a flatter rotation curve compared to the Newtonian model (see Figure 2). The key difference to LCDM is that instead of the flat curve being as a result of an invisible dark matter halo, the flat curve is due to the asymmetry in the matter and antimatter distributions. In particular, the antimatter clouds create a gravitational field at the outskirts of the galaxies that introduces an additional acceleration of order 10^{-11} m/s^{2} to 10^{-10} m/s^{2}, which compares well with the accepted MOND value of ~ 1.2 x 10^{-10} m/s^{2}.

### Pushing the Boundaries

The key result is that the polarisation between the matter and antimatter components of a Dirac-Milne universe is consistent with the gravitational polarisation required by MOND. Flat rotation curves are created naturally, thanks to the antimatter clouds, without needing to invoke dark matter. One important difference is that the MOND acceleration parameter is meant to be a constant, while the authors of this study show that in a Dirac-Milne universe, the extra acceleration changes according to redshift and is therefore not a fundamental constant. They also show that the value decreases over time, suggesting that structure formation is slowing. Previous studies have shown that Dirac-Milne cosmology is concordant with properties such as distance measures, age, structure formation and nucleosynthesis. This study adds rotation curves to the list. With dark matter remaining elusive, cosmological models like the Dirac-Milne universe and frameworks such as MOND continue to offer alternative, thought-provoking descriptions of the Universe.

Featured image credit: Chardin et al., 2021

Edited by: Abygail Waggoner

*The author would like to acknowledge the Whadjuk peoples of the Noongar nation, the traditional custodians of the land on which this post was written, and pays respects to Elders past and present.*

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Are you saying that a classical Newtonian calculation using the Dirac-Milne hypothesis of antimatter halos gives roughly the same result as a Modified Newtonian formulation when the latter calculation is made on the matter galaxies that have no Dark Matter?

If that’s the case, we then have three alternatives: Dark Matter, MOND, and Dirac-Milne. Correct?

Thank you.