Cosmic Collider Gravitational Waves sourced by Right-handed Neutrino production from Bubbles: Testing Seesaw, Leptogenesis and Dark Matter

We study a minimal type-I seesaw framework in which a first-order phase transition (FOPT), driven by a singlet scalar, produces right-handed neutrinos (RHNs) through bubble collisions, realizing a cosmic-scale collider that probes ultra-high energy scales. The resulting RHN distribution sources novel low-frequency gravitational-waves (GWs) in addition to the standard bubble-collision contribution. A stable lightest RHN can account for the observed dark matter (DM) relic abundance for masses as low as $M_{1} \equiv m_{\rm DM} \gtrsim 10^{6},\mathrm{GeV}$, with the associated novel GW signal accessible in LISA, ET and upcoming LVK detectors. If the RHNs are unstable, their CP-violating decays generate the observed baryon asymmetry via leptogenesis for $M_{1} \gtrsim 10^{11},\mathrm{GeV}$ and phase transition temperatures $T_* \gtrsim 10^{6},\mathrm{GeV}$, for which the novel GW spectrum is detectable in ET, BBO and upcoming LVK. If RHN decays also populate a dark-sector fermion with mass $m_χ \in [10^{-4},10^{4}],\mathrm{GeV}$, successful co-genesis of baryons and asymmetric dark matter occurs for $T_* \gtrsim 10^{7},\mathrm{GeV}$ and $M_{1} \gtrsim 10^{9},\mathrm{GeV}$, naturally explaining $Ω_{\rm DM} \simeq 5Ω_{\rm B}$. The corresponding GW signals are testable with LISA, ET, and BBO. Finally, we analyze a UV-complete multi-Majoron model, based on a global $U(1)N \times U(1){\rm B-L}$ extension, motivated from the hierarchy of lepton masses, which we dub as Mojaron collider. The corresponding FOPT in this model leaves a distinctive GW signature arising from RHN production during $U(1)_N$ symmetry breaking detectable by BBO, ET and upcoming LVK. Successful leptogenesis is realized for heaviest RHN mass $M_3 \sim 10^{10},\mathrm{GeV}$ and a $U(1)_N$ breaking vev $v_2 \sim \mathcal{O}(\mathrm{TeV})$, which sets the seesaw scale.

💡 Research Summary

The paper investigates a minimal type‑I seesaw extension of the Standard Model in which a singlet scalar ϕ drives a strong first‑order phase transition (FOPT). In the runaway regime, bubble walls accelerate to ultra‑relativistic speeds, and the collision of these walls converts a sizable fraction of the vacuum energy into particles rather than solely into scalar field gradients. The authors develop a formalism based on the imaginary part of the effective action to compute the probability of particle production from the classical background field ϕ(x,t). By Fourier‑decomposing the wall configuration, they express the number density of produced particles in terms of an efficiency factor f(p²) and the imaginary part of the two‑point 1PI Green’s function Im Γ⁽²⁾(p²). For runaway transitions, the efficiency factor exhibits a universal p⁻⁴ power‑law component (originating from the non‑trivial dynamics of the field during collision) multiplied by a Gaussian peak centred on the scalar mass in the relevant vacuum.

Applying this framework to fermionic final states, the authors focus on the Yukawa interaction y ϕ N N, where N denotes right‑handed neutrinos (RHNs). They show that bubble collisions can non‑thermally produce a large population of RHNs with typical energies far above the ambient temperature T*. This “cosmic collider” can reach energies up to the Planck scale in principle, but the relevant phenomenology is explored for RHN masses in the range 10⁶–10¹⁰ GeV.

Two distinct cosmological outcomes are considered:

1. Stable RHN as Dark Matter (DM).
   If the lightest RHN (N₁) is absolutely stable, its non‑thermal abundance can account for the observed dark matter relic density provided M₁ ≳ 10⁶ GeV. The relic density is set by the efficiency of bubble‑induced production and subsequent dilution from the expansion of the Universe. Importantly, the inhomogeneous RHN distribution sources an additional stochastic gravitational‑wave (GW) background, distinct from the standard bubble‑collision signal. This “RHN‑sourced” GW exhibits a low‑frequency power‑law spectrum (Ω_GW h² ∝ f⁻¹) that can be probed by space‑based interferometers (LISA) and ground‑based detectors (ET, upcoming LVK runs). In parts of parameter space the RHN‑sourced GW dominates over the conventional bubble‑collision contribution.

2. Unstable RHN and Leptogenesis.
   If N₁ decays via CP‑violating channels N → ℓ H, it can generate the observed baryon asymmetry through thermal‑like leptogenesis, even though the RHNs are produced non‑thermally. The authors derive a “diamond condition” requiring M₁ ≳ 10¹¹ GeV and a phase‑transition temperature T* ≳ 10⁶ GeV to achieve η_B ≃ 6 × 10⁻¹⁰. The same bubble‑induced production yields a GW spectrum that is comparable to or louder than the standard signal, making it observable with ET, BBO and future LVK runs.

The paper further extends the scenario to asymmetric dark matter (AsDM). By introducing a dark‑sector fermion χ (mass 10⁻⁴–10⁴ GeV) that couples to RHNs, the decays N → χ ϕ and N → ℓ H simultaneously generate lepton and dark‑sector asymmetries of comparable magnitude. This co‑genesis framework works for M₁ ≳ 10⁹ GeV and T* ≳ 10⁷ GeV, naturally reproducing the empirical relation Ω_DM ≈ 5 Ω_B. The associated GW signal retains the low‑frequency power‑law shape, with detectable amplitudes for LISA (mHz) and ET/BBO (Hz) bands.

To embed the setup in a UV‑complete theory, the authors construct a multi‑Majoron model based on a global U(1)N × U(1){B‑L} symmetry. Two singlet scalars acquire vacuum expectation values, breaking the symmetries at distinct scales: v₁ (∼10⁹ GeV) for B‑L and v₂ (∼TeV) for U(1)_N. The breaking of U(1)_N triggers a strong FOPT, with bubble collisions again producing right‑handed neutrinos, now specifically the heaviest state N₃ with mass M₃ ∼ 10¹⁰ GeV. This “Majoron collider” yields a characteristic GW signature: a distinct peak and spectral shape that differs from the generic bubble‑collision template, allowing future detectors (BBO, ET, LVK) to discriminate the model. Successful leptogenesis is achieved with M₃ ∼ 10¹⁰ GeV and v₂ ∼ TeV, fixing the seesaw scale.

Throughout the manuscript, the authors compute the GW signal‑to‑noise ratio (SNR) for various detector configurations, showing that LISA, ET, BBO and upcoming LVK runs can probe large swaths of the parameter space. They also note that existing LVK O3 data already exclude parts of the high‑amplitude region.

In summary, the work establishes a novel connection between first‑order phase transitions, non‑thermal right‑handed neutrino production, and multiple cosmological relics (dark matter, baryon asymmetry, asymmetric dark matter). It demonstrates that the additional GW component sourced by the produced RHNs provides a powerful, complementary probe of ultra‑high‑scale physics—potentially reaching the seesaw and leptogenesis scales that are otherwise inaccessible to laboratory experiments. The multi‑Majoron UV completion further illustrates how such phenomena can arise naturally from well‑motivated global symmetries, offering concrete targets for upcoming gravitational‑wave observatories.