The Dark Matter Conundrum: A Vacuum Solution

For decades, astronomers have been haunted by a mathematical ghost: 95% of the cosmos is missing. To make the universe make sense, we invented Dark Matter and Dark Energy—invisible phantoms that hold galaxies together and push the fabric of space apart.

What if these phantoms don't actually exist? What if the "missing" mass is simply a trick of the vacuum itself?

The Provocative Alternative: A Polarized Vacuum

A theoretical model by Dragan Slavkov Hajdukovic suggests we have been hunting for particles that aren't there. Instead, it proposes that the quantum vacuum is not empty but a medium that can be polarized by gravity.

The Core Proposal

The theory reclassifies the quantum vacuum, the "empty" space between stars, as an active medium. It argues that the effects we attribute to dark matter are not caused by unseen particles but are the result of the vacuum itself reacting to the gravitational pull of the normal, baryonic matter we can observe.

Why It Matters: Solving a Cosmic Mismatch

For the average person, this idea is significant because it promises to solve the "cosmological constant problem".

The Staggering Discrepancy

Current physics faces a massive conflict between observation and theory.

Observed Vacuum Energy Density: An incredibly small value: $< 10^{-26} \text{ kg/m}^3$ .
Theoretical Prediction: Quantum theory predicts a vacuum energy density over 120 orders of magnitude larger.

By redefining how the vacuum behaves, this model could finally align the physics of the very small (quantum) with the physics of the very large (cosmology).

The Radical Engine: Antimatter Gravity

The entire theory rests on one radical assumption about the fundamental nature of antimatter.

The Foundational "If"

The model's engine is the hypothesis that antimatter might have a "negative" gravitational charge. If true, matter and antimatter would gravitationally repel each other.

This would cause the virtual particle-antiparticle pairs that constantly flicker in and out of existence within the quantum vacuum to act as tiny gravitational dipoles.

How It Explains a Galaxy

When these gravitational dipoles surround a massive object like a galaxy, they align. This creates a "polarized vacuum" that generates an extra gravitational force, mimicking dark matter.

A Calculated Prediction

For a galaxy like the Milky Way, the model makes a precise, testable prediction:

Baryonic (Normal) Mass: $3.8 \times 10^{41} \text{ kg}$
Predicted "Dark Matter" Halo Mass: $1.8 \times 10^{42} \text{ kg}$

This predicted ratio is not arbitrary. The model suggests the universal ratio of normal matter to dark matter is a fixed geometric constant: $2/3\pi^2$ , or approximately 0.212.

The Crucial Caveats: Is the Hunt Over?

Despite its elegance, this "Toy Model" faces significant challenges and remains a theoretical framework.

Major Theoretical Hurdle

The core assumption—antimatter falling "up"—explicitly violates the Weak Equivalence Principle, a cornerstone of Einstein’s theory of general relativity. Experiments like AEGIS at CERN are actively working to measure antimatter's weight, but definitive proof of gravitational repulsion is still lacking.

Simplifications and Limitations

The model also relies on significant simplifications:

It treats complex spiral galaxies as simple spheres.
It uses estimated constants, like the pion Compton wavelength ( $\lambda_\pi$ ), to set its scale.

Until the antimatter hypothesis is proven, this elegant solution remains a compelling mathematical "what if."

Reference:
Title: Dark matter, dark energy and gravitational properties of antimatter
Author: Dragan Slavkov Hajdukovic (CERN, PH Division)
Note: Preprint/Internal Report; later published in Astrophysics and Space Science, 2011.