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A Model of Dark Matter and Energy

This paper proposes a classical cosmological model in which electrically charged, extremely massive dark matter replaces dark energy, naturally yielding a cosmological constant comparable to the mean matter density without the need for fine-tuning.

Original authors: Paul H. Frampton

Published 2026-01-26

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Paul H. Frampton

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine the universe as a giant, expanding balloon. For decades, scientists have been puzzled by two big mysteries about this balloon:

The "Dark" Stuff: We know there is invisible stuff holding galaxies together (Dark Matter) and invisible stuff pushing the balloon to expand faster (Dark Energy).
The "Cosmological Constant": There is a specific number in physics that describes the energy of empty space. It's incredibly small, and scientists have struggled to explain why it is that tiny number.

This paper, by Paul Frampton, proposes a radical new way to look at these mysteries. It suggests that Dark Energy doesn't exist as a separate thing at all. Instead, it is actually just a specific part of Dark Matter acting in a very strange way.

Here is the story of the paper, broken down with simple analogies.

1. The Four-Layer Cake of the Universe

The author suggests that the universe isn't ruled by the same force everywhere. Imagine the universe as a four-layer cake, where the "flavor" of physics changes as you get bigger or smaller:

Layer 1 (The Biggest Scale): The entire universe. Here, Electricity is the boss.
Layer 2 (Galaxies & Solar Systems): This is where we live. Here, Gravity is the boss.
Layer 3 (Atoms & Molecules): Back to Electricity being the boss.
Layer 4 (The tiniest particles): Here, the Strong and Weak nuclear forces join the party.

The author points out that Gravity (Layer 2) is "sandwiched" between two layers of Electricity. This is unusual, but it sets the stage for the main idea.

2. The "Super-Charged" Ghosts

The paper proposes that the "Dark Matter" holding galaxies together is made of heavy, invisible black holes. But there is a second, even stranger type of Dark Matter that fills the space between galaxies.

The author calls these PEMNSs (Primordial Extremely Massive Naked Singularities).

What are they? Imagine a black hole, but instead of having an "event horizon" (a point of no return), it is "naked." It's a singularity exposed to the universe.
The Twist: These aren't just heavy; they are electrically charged. They all have the same type of charge (like having a negative charge).

3. The Balloon Analogy: Why the Universe is Expanding

In the standard view, "Dark Energy" is a mysterious force that pushes the universe apart.

In this paper's view, the universe is expanding because of Coulomb Repulsion.

The Analogy: Imagine you have a room full of people, and everyone is holding a balloon with a negative charge. Because they all have the same charge, they naturally push away from each other.
The Result: These "Super-Charged Ghosts" (PEMNSs) are so massive and so far apart that their electric repulsion pushes the universe apart. This push looks exactly like Dark Energy, but it's actually just electricity doing its job on a cosmic scale.

4. Solving the "Tiny Number" Mystery

Scientists have been confused about why the energy of empty space (the Cosmological Constant) is so small.

The Paper's Claim: It's not a mystery at all. The author calculates that the average density of matter in the universe is almost exactly the same as this "tiny" energy number.
The Takeaway: The value isn't "surprisingly small"; it's just the natural weight of the universe. The paper argues this has nothing to do with quantum mechanics (the physics of tiny particles) but is a result of the universe's mass and size.

5. A Brighter Future for the Universe

The paper also looks at the "fate" of the universe.

The Old View (Standard Model): If Dark Energy keeps pushing forever, the universe will expand so fast that in a trillion years, every galaxy will disappear from our view. We will be alone in the dark, unable to see anything else. Cosmology (the study of the universe) would become impossible.
The New View (This Paper): Because the "push" comes from charged matter that gets weaker as the universe expands, the acceleration will slow down.
The Result: In a trillion years, we won't be alone. We will still be able to see billions of other galaxies. The universe will remain a place where we can study the stars, rather than a lonely, dark void.

Summary

The paper argues that we don't need a mysterious "Dark Energy" to explain the universe's expansion. Instead, the universe is filled with super-massive, electrically charged black holes that are pushing each other apart. This explains the expansion, solves the mystery of the cosmological constant's value, and ensures that the universe remains a visible, interesting place for billions of years to come.

Note: The author admits these ideas are counter-intuitive (it feels weird that electricity rules the biggest scale while gravity rules our local neighborhood), but claims the math holds up without any fatal flaws.

Technical Summary: Model of Dark Matter and Energy

Problem Statement
The paper addresses two fundamental puzzles in theoretical cosmology: the nature of the cosmological constant ( $\Lambda$ ) and the composition of the universe's energy density. Specifically, it seeks to explain why the observed value of $\Lambda$ is of the order $(meV)^4$ without requiring fine-tuning, and to resolve the energy budget discrepancy where standard models posit 5% normal matter, 25% dark matter, and 70% dark energy. The author challenges the conventional wisdom that dark energy is a distinct entity responsible for accelerated expansion, proposing instead that it is a misidentified component of dark matter.

Methodology
The author constructs a classical cosmological model that operates without the Planck constant ( $\hbar$ ), effectively setting the Planck mass to zero. This approach posits that the observed cosmological constant has no connection to quantum mechanics. The model is built upon a specific hierarchy of length scales where the dominant forces vary:

Largest Scale (Universe): Electromagnetism dominates.
Intermediate Scale (Galaxies/Clusters): Gravity dominates.
Atomic/Molecular Scale: Electromagnetism dominates.
Sub-nuclear Scale: Strong and weak interactions join electromagnetism.

The model introduces three distinct matter components:

Old Dark Matter: Composed of Primordial Intermediate Mass Black Holes (PIMBHs, $100M_\odot$ to $10^5M_\odot$ ) and Primordial Supermassive Black Holes (PSMBHs, $10^7M_\odot$ ) located in galactic centers.
New Dark Matter: Composed of Primordial Extremely Massive Naked Singularities (PEMNSs). These are modeled as super-extremal Reissner-Nordström (RN) black holes with masses $M_{PEMNS} \approx 10^{12}M_\odot$ and large negative electric charges ( $Q \approx -4 \times 10^{32}$ Coulombs).
Normal Matter: Standard baryonic matter.

The methodology involves calculating the stress-energy tensor contributions from both the gravitational field (using the RN metric) and the electromagnetic field of the PEMNSs. The author utilizes a wide-separation expansion ( $1/r$ ) given that the mean separation of PEMNSs is a few parsecs while their Schwarzschild radii are $\sim 0.1$ pc. The paper also evaluates the entropy of the universe, comparing the contributions of black holes against the holographic maximum entropy bound.

Key Contributions and Results

Reinterpretation of Dark Energy: The model proposes that "Dark Energy" is actually 70% of the "Dark Matter" sector, specifically the component composed of PEMNSs. The accelerated expansion of the universe is attributed not to a repulsive gravitational force (which contradicts the assumption of attractive gravity), but to the Coulomb repulsion between these highly charged, massive singularities.
Derivation of the Cosmological Constant: By summing the gravitational and electromagnetic stress-energy tensors, the author derives an effective cosmological constant:
$\Lambda \sim + O((meV)^4)$
This value emerges naturally without fine-tuning and is shown to be consistent with the observed mean mass density of the universe ( $\rho_U$ ).
Equation of State: The model predicts an equation of state parameter $\omega = P/\rho$ extremely close to $-1$:
$\omega = -1 \pm O(10^{-14})$
This deviation is attributed to the $1/r$ expansion terms and is considered unobservable given the magnitude of Cosmic Microwave Background (CMB) perturbations.
Entropy and Holographic Bound: The paper calculates the entropy contribution of the PEMNSs. While PSMBHs and PIMBHs contribute $\sim 10^{103}$ (in units of $k$ ), the addition of PEMNSs raises the total entropy to $\sim 10^{113}$ . This is a significant step toward the holographic maximum entropy bound of $\sim 10^{123}$ , suggesting that the universe contains missing high-entropy components.
Time Dependence and Future Evolution: Unlike the $\Lambda$ $Λ$ CDM model, where the cosmological constant is static and the "extroverse" (the region beyond the observable horizon) expands exponentially to infinity, the PEMNS model predicts a time-dependent $\Lambda(t)$ $Λ (t)$ . As the universe expands, the density of charged dark matter decreases, causing $\Lambda(t)$ $Λ (t)$ to decay as $t^{-2}$ $t^{- 2}$ . Consequently, the scale factor behaves as matter-dominated ( $a(t) \sim t^{2/3}$ $a (t) \sim t^{2/3}$ ) in the far future.
- Implication: In the $\Lambda$ CDM scenario, the observable universe would eventually contain only the Milky Way, rendering cosmology impossible. In the PEMNS model, the expansion is slower, allowing roughly 180 billion galaxies to remain observable even a trillion years in the future, preserving the possibility of observational cosmology.

Significance and Claims
The paper claims to offer a novel resolution to the dark matter/energy dichotomy by unifying them under a single sector of primordial black holes and naked singularities. Its primary significance lies in:

Eliminating Dark Energy: It argues that dark energy does not exist as a separate entity but is a misidentification of a charged dark matter component.
Naturalness of $\Lambda$ : It asserts that the smallness of the cosmological constant is not a mystery requiring quantum gravity or string theory explanations, but is simply a reflection of the universe's mean mass density, calculable without $\hbar$ .
Force Hierarchy: It challenges the assumption that gravity dominates at all large scales, proposing that electromagnetism governs the largest cosmological scales due to the presence of charged naked singularities.

The author acknowledges that the existence of naked singularities violates the unproven cosmic censorship hypothesis and that the model relies on a simplified view of the universe. However, the paper posits that the consistency of the "sandwich" structure of force dominance and the entropy arguments provide a compelling, albeit counterintuitive, alternative to standard cosmological models.