Baryon-dark matter coincidence in Randall-Sundrum Model

This paper demonstrates that within the Randall-Sundrum extra-dimensional framework, where Standard Model and dark matter fields reside on the IR brane and interact via graviton and radion portals, the observed dark matter relic abundance and baryon asymmetry can be simultaneously explained through freeze-in production and TeV-scale leptogenesis, respectively, while satisfying cosmological constraints and being subject to current LHC graviton search limits.

The Gist

The Big Picture: Two Mysteries, One Solution

Imagine the universe is a giant puzzle with two missing pieces that don't seem to fit together:

1. Dark Matter: We know it's there because it holds galaxies together with gravity, but we can't see it or touch it. It's like a ghost that only pushes on things.
2. The Matter-Antimatter Mystery: When the universe began, it should have created equal amounts of matter (us) and antimatter (which destroys matter). If that happened, everything would have cancelled out, leaving nothing but light. But we are here. Something tipped the scales to create more matter.

This paper proposes a single "magic key" that unlocks both mysteries at the same time, using a theory called the Randall-Sundrum (RS) Model.

The Setting: A Warped Universe

To understand the solution, imagine the universe isn't just a flat sheet of paper (4 dimensions). Instead, imagine it's a warped canyon (5 dimensions).

• The Branes: Think of our entire visible universe (stars, planets, you, me) as a thin sheet of paper stuck to the bottom of this canyon (the "IR brane").
• The Bulk: The space inside the canyon is called the "bulk."
• The Gravity Leak: In this model, most things (like light and atoms) are stuck to our sheet of paper. But Gravity is special. It can leak out into the canyon and travel through the bulk.

Because the canyon is "warped" (curved like a funnel), gravity gets weaker as it travels up the canyon and stronger as it comes down to our sheet. This warping explains why gravity feels so weak to us compared to other forces, solving a major headache in physics called the "Hierarchy Problem."

The Characters: The Messengers

In this warped canyon, there are two special messengers that can travel between the "Dark Sector" (where Dark Matter lives) and the "Visible Sector" (where we live):

1. The Graviton: The particle that carries gravity. In this model, it has heavy "cousins" called Kaluza-Klein (KK) gravitons that live in the bulk.
2. The Radion: Think of this as a "breathing particle." It represents the size of the canyon itself. If the canyon expands or shrinks slightly, the radion vibrates. It can also travel between the two sectors.

The Story: How We Got Here

1. Creating Dark Matter (The "Freeze-In" Recipe)

Usually, scientists thought Dark Matter was made like a hot soup where particles bump into each other until they settle down. But recent experiments haven't found Dark Matter that way.

This paper suggests a different recipe called "Freeze-In."

• The Analogy: Imagine a room (the early universe) that is very hot. You have a door that is almost completely shut, with just a tiny crack.
• The Process: Very slowly, a few particles sneak through that tiny crack from the hot room into a cold, empty room next door. They never get enough energy to come back out.
• The Result: Over time, just enough particles accumulate in the cold room to fill it up perfectly.
• In the Paper: The "tiny crack" is the interaction between our world and the Dark Matter world, mediated by the Graviton and Radion. Because these messengers interact so weakly, the Dark Matter never gets "hot" or mixes with us; it just slowly "freezes in" from the heat of the early universe. The paper shows that with the right settings for the canyon's shape, this process creates exactly the amount of Dark Matter we see today.

2. Creating the Matter-Antimatter Imbalance (Leptogenesis)

Now, how do we explain why we have more matter than antimatter?

• The Analogy: Imagine a factory producing two types of widgets: "Good" (matter) and "Bad" (antimatter). Usually, the machine makes them 50/50.
• The Twist: In this model, the factory produces heavy, unstable particles called Right-Handed Neutrinos. Because of the warped canyon, these particles are much lighter than they would be in a normal universe (down to the "TeV" scale, which is accessible by our particle colliders).
• The Decay: These heavy neutrinos are unstable. They decay (break apart) into other particles. Because of a quirk in the laws of physics (CP violation), they break apart slightly more often into "Good" widgets than "Bad" ones.
• The Result: This tiny imbalance gets amplified, leaving us with a universe full of matter. The paper shows that the same warped geometry that helps create Dark Matter also allows these neutrinos to exist at the right energy levels to create the imbalance we see today.

The Connection: Why It Matters

The most exciting part of this paper is the coincidence.

• In many theories, you have to tweak the numbers separately to get the right amount of Dark Matter and the right amount of Matter/Antimatter.
• In this "Warped Canyon" model, the same settings (the shape of the canyon and the mass of the messengers) naturally produce both results simultaneously. It's like finding a single dial that, when turned, sets the volume for both the bass and the treble perfectly at the same time.

The Catch: The Collider Test

The paper doesn't just stay in theory; it checks if this idea survives real-world tests.

• The LHC: The Large Hadron Collider (LHC) smashes particles together to look for these heavy "cousin" gravitons.
• The Constraint: The paper calculates that if this model is true, the LHC should have already seen signs of these heavy gravitons or the radion. If the LHC doesn't see them, it puts strict limits on how hot the early universe was allowed to get (the "reheating temperature").
• The Conclusion: The paper finds a "sweet spot." There is a specific range of temperatures and particle masses where:
  1. The Hierarchy Problem is solved.
  2. We get the right amount of Dark Matter.
  3. We get the right amount of Matter/Antimatter.
  4. We haven't been ruled out by the LHC yet.

Summary

This paper suggests that our universe is a warped 5-dimensional canyon. In this canyon, gravity and a "breathing" particle (the radion) act as tiny bridges. These bridges slowly leak energy to create Dark Matter and tip the scales to create the matter we are made of. It's a unified story where the shape of the universe explains why we exist and why the "ghost" of Dark Matter is there, all while keeping an eye on what our giant particle smashers are telling us.

Technical Summary

Technical Summary: Baryon-dark matter coincidence in Randall-Sundrum Model

Problem Statement
The paper addresses two fundamental open questions in cosmology and particle physics: the nature of Dark Matter (DM) and the origin of the Baryon Asymmetry of the Universe (BAU). While astrophysical evidence confirms the existence of DM, its particle nature and interaction strength with the Standard Model (SM) remain unknown. Purely gravitational production of DM typically requires extremely high reheating temperatures ($T_{rh} \gtrsim 10^{15}$ GeV) due to the weakness of the Planck-scale coupling. Conversely, explaining the BAU via standard thermal leptogenesis typically requires heavy right-handed neutrinos (RHNs) with masses $M_N \gtrsim 10^9$ GeV, also implying high reheating temperatures. Furthermore, the "hierarchy problem"—the vast disparity between the electroweak scale and the Planck scale—remains unresolved in the SM. The authors investigate whether a unified framework can simultaneously resolve the hierarchy problem, generate the observed DM relic abundance via a non-thermal mechanism, and produce the BAU, all while remaining consistent with current collider and cosmological constraints.

Methodology
The authors employ the Randall-Sundrum (RS) warped extra-dimensional model as the theoretical framework. In this setup:

1. Geometry: The universe is a slice of five-dimensional anti-de Sitter space ($AdS_5$) bounded by two 3-branes (UV and IR). The SM fields are confined to the IR brane, while gravity propagates in the bulk.
2. Mediators: The model predicts a tower of Kaluza-Klein (KK) gravitons and a scalar radion field (fluctuation of the inter-brane distance). These fields act as portals between the visible sector and the dark sector.
3. Dark Matter Candidates: The study considers three distinct DM candidates residing on the IR brane: a gauge-singlet scalar ($S$), a Majorana fermion ($\Psi$), and a massive vector boson ($X_\mu$). These are stabilized by a $Z_2$ symmetry.
4. Production Mechanism: The authors analyze the freeze-in production of DM. Unlike freeze-out, the DM sector never reaches thermal equilibrium. DM is produced via the decay or scattering of SM particles mediated by the radion and KK gravitons. The interaction strength is suppressed by the effective scale $\Lambda_r \sim \text{TeV}$, rather than the Planck mass.
5. Baryogenesis: The framework incorporates Type-I seesaw leptogenesis. RHNs are introduced on the IR brane. Their masses are warped down to the TeV scale. To generate sufficient BAU at this low scale, the authors utilize resonant leptogenesis, where the CP asymmetry is enhanced by the near-degeneracy of the first two RHN masses.
6. Constraints: The parameter space is constrained by:
   • Collider limits: LHC searches for diphoton resonances (KK gravitons) and radion-Higgs mixing.
   • Cosmology: Big Bang Nucleosynthesis (BBN) bounds on reheating temperature, limits on extra radiation ($\Delta N_{eff}$) from Planck data, and the requirement that DM production remains in the freeze-in regime (avoiding thermalization).

Key Contributions and Results

• Unified Resolution of Hierarchy and DM: The authors demonstrate that the RS framework naturally addresses the hierarchy problem by warping the fundamental Planck scale down to the TeV scale on the IR brane. Within this same setup, they show that the observed DM relic abundance ($\Omega_{DM}h^2 \approx 0.12$) can be achieved via freeze-in production mediated by the radion and KK gravitons.
• Low Reheating Temperature: A primary result is that the observed DM abundance can be reproduced for reheating temperatures as low as $T_{rh} \lesssim 10^5$ GeV (and even lower for lighter DM), significantly below the $10^{15}$ GeV required for purely gravitational freeze-in in 4D. This is achieved because the effective coupling is enhanced by the warped geometry ($\Lambda_r \sim \text{TeV}$).
• TeV-Scale Leptogenesis: The study shows that the same warped geometry allows for RHNs with masses in the TeV range. By invoking resonant leptogenesis, the model successfully generates the observed BAU ($Y_B \approx 8.75 \times 10^{-11}$) without requiring the high-scale Davidson-Ibarra bound ($M_N \gtrsim 10^9$ GeV).
• Baryon-DM Coincidence: The paper establishes a "coincidence" where the same reheating temperature range ($T_{rh} \gtrsim 500$ GeV) required to produce the RHNs for leptogenesis is sufficient to generate the correct DM abundance via freeze-in. This provides a unified explanation for the similar orders of magnitude of baryonic and dark matter densities.
• Collider-Cosmology Complementarity: The authors perform a detailed analysis of LHC constraints (specifically CMS diphoton searches). They find that current LHC bounds on the mass of the first KK graviton ($m_{G1}$) and the effective scale ($\Lambda_r$) impose strong, non-trivial constraints on the allowed reheating temperature. For instance, for a scalar DM of 1 MeV, current data excludes $T_{rh} \lesssim 26$ GeV (for $\tilde{k}=0.01$) and $T_{rh} \lesssim 15.8$ GeV (for $\tilde{k}=0.1$). This highlights a direct link between collider exclusion limits and early Universe cosmological history.
• $\Delta N_{eff}$ Constraints: The study evaluates the contribution of dark radiation from graviton decays. It finds that for graviton masses $m_G \gtrsim 2$ TeV, the contribution to $\Delta N_{eff}$ remains within current Planck limits, though future experiments (CMB-S4, CMB-HD) could probe lighter masses.

Significance and Claims
The paper claims to provide a coherent, unified resolution to the hierarchy problem, the DM abundance, and the BAU within a single minimal extension of the SM (the RS model with a radion).

• Novelty: Unlike previous works focusing solely on DM production or hierarchy resolution, this study explicitly links the generation of DM and BAU in the RS context, demonstrating that TeV-scale leptogenesis is viable and compatible with freeze-in DM.
• Phenomenological Viability: The authors assert that their benchmark points satisfy all current constraints from the LHC, BBN, and CMB. They emphasize that the model does not require fine-tuning beyond the standard RS setup and that the "coincidence" of DM and baryon densities arises naturally from the shared dependence on the reheating temperature and the warped geometry.
• Experimental Relevance: The paper highlights that the parameter space is not merely theoretical but is actively being probed by current LHC data. The complementarity between collider searches for heavy resonances and cosmological bounds on reheating temperature is presented as a key feature of the model, suggesting that the early Universe's thermal history can be constrained by high-energy collider experiments.

In conclusion, the authors present a scenario where the warped extra dimensions solve the hierarchy problem, facilitate low-scale leptogenesis, and enable the freeze-in production of DM, all while remaining consistent with current observational data and offering testable predictions for future collider and cosmological experiments.