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Fotis Koutroulis, Eugenio Megías, Stefan Pokorski | Physical review. D/Physical review. D. | (2024)
Primary Link DOI Openalex Full text (OA)

Abstract

We propose a setup for the origin of dark matter based on spacetime with a warped extra dimension and three branes: the Planck brane, the TeV brane, at a (few) TeV scale <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:msub><a:mrow><a:mi>ρ</a:mi></a:mrow><a:mrow><a:mi>T</a:mi></a:mrow></a:msub></a:mrow></a:math>, and a dark brane, at a (sub-)GeV scale <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:msub><c:mi>ρ</c:mi><c:mn>1</c:mn></c:msub><c:mo>≲</c:mo><c:mn>100</c:mn><c:mtext> </c:mtext><c:mtext> </c:mtext><c:mrow><c:mi>GeV</c:mi></c:mrow><c:mo>≪</c:mo><c:msub><c:mi>ρ</c:mi><c:mi>T</c:mi></c:msub></c:math>. The Standard Model (SM) is localized in the TeV brane, thus solving the Higgs hierarchy problem, while the dark matter <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mi>χ</e:mi></e:math>, a Dirac fermion with mass <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:msub><g:mi>m</g:mi><g:mi>χ</g:mi></g:msub><g:mo>&lt;</g:mo><g:msub><g:mi>ρ</g:mi><g:mn>1</g:mn></g:msub></g:math>, is localized in the dark brane. The radion, with mass <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:msub><i:mi>m</i:mi><i:mi>r</i:mi></i:msub><i:mo>&lt;</i:mo><i:msub><i:mi>m</i:mi><i:mi>χ</i:mi></i:msub></i:math>, interacts strongly [<k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:mrow><k:mo>∼</k:mo><k:msub><k:mrow><k:mi>m</k:mi></k:mrow><k:mrow><k:mi>χ</k:mi></k:mrow></k:msub><k:mo>/</k:mo><k:msub><k:mrow><k:mi>ρ</k:mi></k:mrow><k:mrow><k:mn>1</k:mn></k:mrow></k:msub><k:mo>∼</k:mo><k:mi mathvariant="script">O</k:mi><k:mo stretchy="false">(</k:mo><k:mn>1</k:mn><k:mo stretchy="false">)</k:mo></k:mrow></k:math>] with dark matter and very weakly (<p:math xmlns:p="http://www.w3.org/1998/Math/MathML" display="inline"><p:mo>∼</p:mo><p:msub><p:mi>m</p:mi><p:mi>f</p:mi></p:msub><p:msub><p:mi>ρ</p:mi><p:mn>1</p:mn></p:msub><p:mo>/</p:mo><p:msubsup><p:mi>ρ</p:mi><p:mi>T</p:mi><p:mn>2</p:mn></p:msubsup><p:mo>≪</p:mo><p:mn>1</p:mn></p:math>) with the Standard Model matter <r:math xmlns:r="http://www.w3.org/1998/Math/MathML" display="inline"><r:mi>f</r:mi></r:math>. The generic conflict between the bounds on its detection signatures and its proper relic abundance is avoided as dark matter annihilation is <t:math xmlns:t="http://www.w3.org/1998/Math/MathML" display="inline"><t:mi>p</t:mi></t:math>-wave suppressed. The former is determined by its very weak interactions with the SM and the latter by its much stronger annihilation into radions. Therefore, there is a vast range in the dark matter’s parameter space where the correct relic abundance is achieved consistently with the existing bounds. Moreover, for the dark brane with <v:math xmlns:v="http://www.w3.org/1998/Math/MathML" display="inline"><v:msub><v:mi>ρ</v:mi><v:mn>1</v:mn></v:msub><v:mo>≲</v:mo><v:mn>3</v:mn><v:mtext> </v:mtext><v:mtext> </v:mtext><v:mi>GeV</v:mi></v:math>, a confinement/deconfinement first order phase transition, where the radion condensates, produces a stochastic gravitational wave background at the nanohertz frequencies, which can be identified with the signal detected by the Pulsar Timing Array (PTA) experiments. In the PTA window, for <x:math xmlns:x="http://www.w3.org/1998/Math/MathML" display="inline"><x:mn>0.15</x:mn><x:mo>≲</x:mo><x:msub><x:mi>m</x:mi><x:mi>χ</x:mi></x:msub><x:mo>≲</x:mo><x:mn>2</x:mn><x:mtext> </x:mtext><x:mtext> </x:mtext><x:mi>GeV</x:mi></x:math> the relic abundance is reproduced and all constraints are satisfied. Published by the American Physical Society 2024

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Sample Definition And Size

The study proposes a theoretical model involving a warped extra-dimensional spacetime with three branes: the Planck brane, the TeV brane (at a few TeV scale), and a dark brane (at sub-GeV to ~100 GeV scale). Dark matter is modeled as a Dirac fermion χ localized on the dark brane, with mass m_χ < ρ₁. No empirical sample size is involved, as this is a theoretical physics model rather than an experimental or observational study. The paper is not a meta-analysis or literature review.

Study Type

This is a theoretical model-building study in high-energy physics, specifically proposing a new framework for dark matter within a warped extra-dimensional scenario involving three branes. It includes analytical derivations and phenomenological implications.

Conflicts Of Interest

No conflicts of interest are declared in the publication. The article is published under the Creative Commons Attribution 4.0 International license and funded by SCOAP³, with no competing interests noted.

Results Summary

Key findings include: (1) Dark matter annihilation is p-wave suppressed, allowing consistency between relic abundance and detection constraints due to strong annihilation into radions and very weak interactions with Standard Model matter. (2) For dark brane scale ρ₁ ≲ 3 GeV, a first-order confinement/deconfinement phase transition produces a stochastic gravitational wave background at nanohertz frequencies, potentially matching signals observed by Pulsar Timing Array experiments. (3) In the PTA window, for 0.15 GeV ≲ m_χ ≲ 2 GeV, the model reproduces the correct relic abundance while satisfying all constraints. No explicit numerical p-values, effect sizes, or confidence intervals are provided, as the results are theoretical and qualitative/parametric in nature.

Referenced In

StarTalk

Season 17, Episode 19: Is Dark Matter Just Regular Matter in Another Universe?

Hey StarTalkians! Neil and Chuck got a treat this week, sitting down with Professor Brian Greene for a chat about hidden dimensions, string theory and Hilbert spaces. In the discussion, Professor Greene explained a little about “brane worlds” and how they interact with gravity:

Exploring Hidden Dimensions with Brian Greene - StarTalk Radio

(from 47:00)

There is a tantalizing question that comes out of all of this: what if dark matter was just regular matter in another brane?

The Basics of String Theory

The “basics” of string theory are actually easy enough to understand if you don’t delve into the math. It posits that, instead of multiple fundamental particles, the fundamental objects of the universe are actually one-dimensional “strings.”

In the same way guitar strings can produce multiple stable pitches, these cosmic strings can also vibrate in several different ways. These different vibrational “modes” lead to the particles in our universe. So like you can pluck out a whole scale along a guitar string, the cosmic strings create the symphony of matter we see around us.

Brane Worlds Explained

A “brane” is like a cosmic “membrane” that occupies some number of dimensions. A 0-dimensional brane is a particle, a 1-dimensional brane is a string, a flat 2D membrane is a 2-brane and so on.

These branes can have more dimensions, and crucially, get much bigger. It’s possible that a multi-dimensional brane got a huge boost of energy and inflated, ultimately forming our universe. There could equally be other brane worlds out there, alongside ours in a higher-dimensional space.  

Strings interact with these higher-dimensional branes. Strings are either closed (connected to itself) or open. The ends of open strings attach to branes, confining them to that brane world. Most of the forces (electromagnetism and the strong and weak nuclear forces) are confined in this way. Gravity, on the other hand, comes from closed strings, which can freely travel through the inter-brane space, leaking out of our universe.  

The “Dark Brane” and Dark Matter

That explains why gravity is so weak, as Brian pointed out. But it might also explain dark matter. Some physicists propose a hypothetical “dark brane”, which is filled with ordinary matter.

Electromagnetism is confined to the brane, so we can’t see this other world. But gravity is not, so maybe we can feel it, as what we call “dark matter.”

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