Low-reheating scenario in dark Higgs inflation and its impact on dark photon dark matter production

This paper proposes a unified framework where a dark Higgs field drives cosmic inflation and a dark photon serves as dark matter, demonstrating that a low-reheating scenario with significant entropy dilution allows for viable WIMP and FIMP candidates consistent with cosmological observations and potentially accessible to current and future experiments.

The Gist

The Big Picture: Two Mysteries, One Solution

Imagine the universe has two massive, unsolved puzzles:

1. The "Missing Mass" Puzzle: We know there is invisible stuff holding galaxies together (Dark Matter), but we don't know what it is.
2. The "Big Bang" Puzzle: We know the universe expanded incredibly fast right after it began (Inflation), but we don't know what drove that expansion.

Usually, scientists try to solve these two puzzles separately. This paper proposes a clever shortcut: What if the same thing solved both?

The authors suggest a "Dark Sector" of the universe—a hidden neighborhood parallel to our own. In this neighborhood, there is a Dark Higgs field (a hidden version of the famous Higgs boson) and a Dark Photon (a hidden version of light).

• The Dark Higgs acts as the engine that pushed the universe to expand (Inflation).
• The Dark Photon is the invisible stuff holding galaxies together (Dark Matter).

The Story of the Universe: A Three-Act Play

To understand how this works, let's imagine the early universe as a giant, chaotic kitchen.

Act 1: The Big Stretch (Inflation)

Right after the Big Bang, the universe was dominated by the Dark Higgs field. Think of this field as a giant, stretched rubber band. It was full of potential energy. When it snapped back, it caused the universe to expand faster than the speed of light for a split second. This is Inflation.

In many theories, this rubber band snaps so hard it creates a massive explosion of heat and particles, instantly filling the universe with energy. But in this paper, the authors suggest a different scenario: The "Low-Reheating" Scenario.

Act 2: The Slow Cook (Low Reheating)

Usually, after the rubber band snaps, the universe gets super hot (like a furnace). But here, the Dark Higgs is very shy. It doesn't want to share its energy with our visible universe immediately. It decays very slowly.

Imagine the universe is a pot of soup.

• Standard Scenario: You turn on the stove to "High." The soup boils instantly.
• This Paper's Scenario: You turn the stove to "Low." The soup heats up very slowly.

Because the universe stays "cool" for a long time, something interesting happens to the Dark Matter (the Dark Photons).

Act 3: The Dilution Effect (The "Entropy" Analogy)

This is the most important part of the paper. Let's use an analogy of making lemonade.

Imagine you have a glass of very strong, concentrated lemonade (Dark Matter).

• In a hot universe: You make the lemonade, and it stays concentrated. If you make too much, it's too strong (too much Dark Matter).
• In this "Low-Reheating" universe: While you are making the lemonade, someone keeps pouring in huge amounts of water (Entropy/Heat from the slow decay of the Dark Higgs).

The Result: The lemonade gets diluted. Even if you started with a lot of Dark Matter, the "water" from the slow heating process washes it out, leaving just the perfect amount.

Why is this cool?
It allows for two types of Dark Matter that were previously thought to be impossible or too weak to detect:

1. The "FIMP" (Feebly Interacting Massive Particle): Imagine a ghost that barely touches anything. Usually, ghosts are so weak they never stick around. But because the universe was "diluting" everything, these ghosts can actually be a bit more "tactile" (have stronger interactions) and still end up with the right amount. This makes them easier to find!
2. The "WIMP" (Weakly Interacting Massive Particle): Imagine a shy person who usually hides. The dilution allows them to be even shyer (weaker interactions) and still be the right amount.

The "Detective Work" (Results)

The authors ran massive computer simulations (like a cosmic video game) to see if this idea holds up. They checked three things:

1. Does it match the Cosmic Microwave Background (CMB)?

   • The Analogy: The CMB is the "baby photo" of the universe.
   • The Result: Yes! The predictions for how the universe looked as a baby (specifically the "spectral index" and "tensor-to-scalar ratio") match the photos taken by telescopes like Planck and BICEP perfectly.

2. Does it fit the "Dark Matter" rules?

   • The Analogy: We know exactly how much Dark Matter exists (about 27% of the universe).
   • The Result: The "dilution" effect (the water pouring into the lemonade) perfectly adjusts the amount of Dark Matter to match what we see today.

3. Can we find it?

   • The Analogy: Can we catch the ghost?
   • The Result:
     • For the FIMP (the ghost), the paper says they might be just strong enough to be caught by current or future experiments (like the LUX-ZEPLIN detector).
     • For the WIMP, they are harder to catch, but the "low reheating" scenario opens up new places to look.

The "Secret Sauce": The Higgs Portal

How does the Dark Higgs talk to our normal Higgs? Through a tiny "doorway" called the Higgs Portal (a mixing angle).

• If the door is wide open, the universe heats up fast (Standard scenario).
• If the door is barely cracked open (a very small mixing angle), the universe heats up slowly (Low-reheating scenario).

The authors found that if the door is just barely cracked, everything works perfectly. It solves the Dark Matter problem, explains Inflation, and avoids breaking the laws of physics (unitarity).

Summary for the Everyday Person

This paper proposes a unified theory where a hidden version of the Higgs field did two jobs:

1. It blew up the universe (Inflation).
2. It created the invisible stuff holding galaxies together (Dark Matter).

The key twist is that the universe cooled down very slowly after the explosion. This slow cooling acted like a giant water hose, diluting the Dark Matter. This dilution allows for Dark Matter particles that interact slightly more strongly than we thought possible, giving us a much better chance of actually detecting them in a lab soon.

It's a "Goldilocks" scenario: The universe wasn't too hot, and the Dark Matter wasn't too weak. It was just right.

Technical Summary

1. Problem Statement

The Standard Model (SM) fails to explain two major cosmological phenomena: the nature of Dark Matter (DM) and the mechanism of Cosmic Inflation. While the SM Higgs field has been proposed as an inflaton, the quartic potential required for inflation is ruled out by CMB data unless a large non-minimal coupling to gravity is introduced, which raises unitarity concerns. Conversely, Dark Matter candidates like Weakly Interacting Massive Particles (WIMPs) and Feebly Interacting Massive Particles (FIMPs) are constrained by null results from direct detection experiments and collider searches.

The paper addresses the challenge of unifying these two sectors within a single framework while resolving the tension between high-energy inflationary predictions and low-energy DM constraints. Specifically, it investigates whether a Dark $U(1)_D$ gauge extension of the SM can simultaneously:

1. Drive successful inflation via the Dark Higgs field.
2. Produce Dark Photon Dark Matter (DPDM) via both WIMP and FIMP mechanisms.
3. Realize a low-reheating temperature scenario, which is crucial for relaxing constraints on DM couplings via entropy dilution.

2. Methodology

Model Framework

The authors propose a minimal extension of the SM involving a dark $U(1)_D$ gauge symmetry.

• Fields: The model includes the SM Higgs ($H$), a Dark Higgs ($\phi_D$), and a Dark Photon ($W_D$).
• Lagrangian: The interaction is governed by kinetic mixing ($\epsilon$) between the dark photon and hypercharge, and a Higgs portal coupling ($\lambda_{HD}$) between the SM and Dark Higgs sectors.
• Symmetry: A charge conjugation symmetry in the dark sector stabilizes the Dark Photon ($W_D$), making it the DM candidate.
• Mass Basis: The physical Higgs bosons ($h_1, h_2$) are mixtures of the SM and Dark Higgs fields, characterized by a mixing angle $\alpha$.

Inflationary Dynamics

• Inflaton: The Dark Higgs field ($\phi_D$) acts as the inflaton, non-minimally coupled to gravity via a term $\xi_D \phi_D^2 R$.
• RG Improvement: The authors incorporate quantum corrections using Renormalization Group Equations (RGEs) to run couplings from the electroweak scale to the inflationary scale. This includes the running of the quartic coupling $\lambda_D$ and the non-minimal coupling $\xi_D$.
• Observables: They calculate the scalar spectral index ($n_s$) and tensor-to-scalar ratio ($r$) using slow-roll parameters up to second order, comparing them against Planck, BICEP/Keck, and ACT data.

Reheating and DM Production

• Low-Reheating Scenario: The paper explores scenarios where the reheating temperature ($T_{reh}$) is significantly lower than the standard high-scale inflation (down to 1 GeV or even 1 MeV). This is achieved via the decay or scattering of the inflaton into SM particles, controlled by the small portal coupling $\lambda_{HD}$.
• Entropy Dilution: A key mechanism is the production of entropy during the prolonged reheating phase. If DM is produced before the universe fully reheats, its abundance is diluted by this entropy, allowing for stronger couplings (in FIMP scenarios) or weaker couplings (in WIMP scenarios) to match the observed relic density ($\Omega_{DM} h^2 \approx 0.12$).
• Boltzmann Equations: The evolution of DM number density is solved numerically using micrOMEGAs. The study distinguishes between:
  • WIMP: Freeze-out mechanism (thermal equilibrium).
  • FIMP: Freeze-in mechanism (non-thermal, never reaches equilibrium).
• Reheating Stages: The authors analyze the reheating dynamics in three stages based on the inflaton potential shape (quadratic $\to$ quartic $\to$ quadratic), calculating $T_{reh}$ for both perturbative decay and scattering processes.

3. Key Contributions

1. Unified Framework: Successfully demonstrates a minimal $U(1)_D$ extension where the Dark Higgs drives inflation and the Dark Photon serves as DM, linking high-energy inflationary physics with low-energy DM phenomenology via RGEs.
2. Low-Reheating Viability: Establishes that $T_{reh}$ as low as 1 GeV (via decay) and 1 MeV (via scattering) is achievable in Dark Higgs inflation. This is a significant departure from SM Higgs inflation, which typically predicts $T_{reh} \sim 10^{13-15}$ GeV.
3. Relaxation of Constraints:
   • FIMP: Entropy dilution allows for stronger dark gauge couplings ($g_D$) than standard freeze-in scenarios, bringing FIMP candidates into the reach of current and future direct detection experiments.
   • WIMP: Allows for weaker couplings to avoid overproduction, expanding the viable parameter space.
4. Unitarity Resolution: Shows that the non-minimal coupling $\xi_D$ required for Dark Higgs inflation can be much smaller (order unity) compared to SM Higgs inflation ($\xi_H \sim 10^4$), thereby avoiding unitarity violation concerns.
5. Multi-Stage Reheating Analysis: Provides a detailed analytical treatment of the reheating process where the inflaton potential transitions between quadratic and quartic forms, deriving specific conditions for decay-dominated vs. scattering-dominated reheating.

4. Results

• Inflationary Observables: The model predicts $n_s$ and $r$ values consistent with Planck, BICEP/Keck, and ACT data. Specifically, the spectral index $n_s$ can reach values favored by recent ACT results ($n_s \approx 0.974$). The tensor-to-scalar ratio $r$ remains below the current bound ($r \leq 0.036$).
• Reheating Temperature:
  • Decay Process: $T_{reh}$ can be as low as 1 GeV for small $\lambda_{HD}$ (small mixing angle).
  • Scattering Process: $T_{reh}$ can reach the MeV scale (near the Big Bang Nucleosynthesis bound) even with relatively large $\lambda_{HD}$, provided reheating ends in the third stage (quadratic potential regime).
• Dark Matter Phenomenology:
  • Parameter Space: A wide range of parameters is allowed for both WIMP and FIMP scenarios.
  • Direct Detection:
    • FIMP: All allowed points lie below the "neutrino floor" and current LUX-ZEPLIN limits, consistent with null results.
    • WIMP: Some parameter points are already probed by LUX-ZEPLIN, but a significant portion remains viable.
  • Indirect Detection:
    • FIMP: Indirect detection signals are below future CTA sensitivities.
    • WIMP: Indirect detection signals are within the projected reach of future CTA runs.
• Coupling Relations: The study confirms that $T_{reh}$ and $g_D$ are inversely related for FIMPs (higher $T_{reh}$ requires lower $g_D$ to avoid overproduction) but directly related for WIMPs in specific regimes due to entropy dilution effects.

5. Significance

This work is significant because it offers a minimal and testable solution to two of the biggest open questions in cosmology. By unifying Dark Higgs inflation with Dark Photon DM, it:

• Revitalizes FIMP searches: It suggests that FIMP DM, previously thought to be undetectable due to extremely weak couplings, could be detectable if the universe underwent a low-reheating phase.
• Provides a concrete inflationary model: It avoids the theoretical pitfalls of SM Higgs inflation (large $\xi$, unitarity issues) while remaining consistent with all current CMB data.
• Guides Future Experiments: The results define specific regions in the $(M_{WD}, g_D, T_{reh})$ parameter space that should be targeted by next-generation direct detection experiments (like LZ, DARWIN) and indirect detection observatories (like CTA).
• Highlights the role of Reheating: It underscores that the details of the reheating epoch (decay vs. scattering, duration, temperature) are not just cosmological background parameters but critical determinants of the particle physics landscape and DM nature.