[Paper Review] Probing Leptogenesis and Pre-BBN Universe with Gravitational Waves Spectral Shapes

Rome Samanta, Satyabrata Datta|arXiv (Cornell University)|Aug 18, 2021

Neutrino Physics Research94 references10 citations

TL;DR

This paper proposes that gravitational wave (GW) spectral shapes—specifically a flat plateau followed by a rising amplitude—can probe leptogenesis in seesaw models with a gauged U(1)B−L symmetry. The signal arises from cosmic strings formed during U(1)B−L breaking, with a stiffer post-inflationary equation of state (ω > 1/3) like kination enhancing both GW amplitude and lepton asymmetry via a two-loop gravitational operator ∂μRjμ. The key result is that a detectable GW signal with a spectral break and rising shape, combined with a potential neutrinoless double beta decay signal, could constrain the lightest right-handed neutrino mass and probe the onset of radiation domination at intermediate scales.

ABSTRACT

On the frequency-amplitude plane, Gravitational Waves (GWs) from cosmic strings show a flat plateau at higher frequencies due to the string loop dynamics in standard radiation dominated post-inflationary epoch. The spectrum may show an abrupt upward or a downward trend beyond a turning point frequency $f_*$, if the primordial dark age prior to the Big Bang Nucleosynthesis (BBN), exhibits non-standard cosmic histories. We argue that such a spectral break followed by a rising GW amplitude which is a consequence of a post-inflationary equation of state ($\omega>1/3$) stiffer than the radiation ($\omega=1/3$), could also be a strong hint of a leptogenesis in the seesaw model of neutrino masses. Dynamical generation of the right handed (RH) neutrino masses by a gauged $U(1)$ symmetry breaking leads to the formation of a network of cosmic strings which emits stochastic GWs. A gravitational interaction of the lepton current by an operator of the form $\partial_\mu R j^\mu$--which can be generated in the seesaw model at the two-loop level through RH neutrino mediation, naturally seeks a stiffer equation of state to efficiently produce baryon asymmetry proportional to $1-3\omega$. We discuss how GWs with reasonably strong amplitudes complemented by a neutrino-less double beta decay signal could probe the onset of the most recent radiation domination and lightest RH neutrino mass at the intermediate scales.

Motivation & Objective

• To investigate whether gravitational wave (GW) spectral shapes can serve as a probe for leptogenesis in seesaw models with a gauged U(1)B−L symmetry.
• To explore how a non-standard cosmic history with ω > 1/3 (e.g., kination) modifies GW spectra from cosmic strings, leading to a rising amplitude after a spectral break.
• To connect the GW signal to the gravitational lepto/baryogenesis mechanism via the ∂μRjμ operator, which generates lepton asymmetry proportional to (1−3ω).
• To demonstrate that a combination of strong GW amplitude and a potential neutrinoless double beta decay signal can constrain the lightest right-handed neutrino mass and the onset of radiation domination.

Proposed method

• Model cosmic string networks formed via U(1)B−L breaking, with string tension μ and energy loss dominated by GW emission.
• Compute GW energy density spectrum using the Nambu–Goto action and loop distribution, assuming scaling evolution and a flat plateau at high frequencies.
• Incorporate a non-standard equation of state (ω > 1/3) such as kination, modifying the Hubble parameter and redshifting the energy density as ρω ∝a−3(1+ω).
• Derive the lepton asymmetry production rate from the two-loop operator ∂μRjμ/M², with asymmetry proportional to ˙R ∝(1−3ω), and solve the Boltzmann equation for B−L number density.
• Use the master formula NfB−L ≈ (κβ)/(8zin⁸) × exp(−4K₁/z∗) to compute the final asymmetry, validated against numerical simulations.
• Combine GW amplitude (ΩGW ∝f⁻δ) and asymmetry predictions to identify observable signatures in LISA, PTAs, and neutrinoless double beta decay experiments.

Experimental results

Research questions

• RQ1 Can a rising gravitational wave spectral shape after a plateau indicate a stiff post-inflationary equation of state (ω > 1/3) in the pre-BBN universe?
• RQ2 Does the presence of cosmic strings from U(1)B−L breaking provide a viable source for detectable primordial gravitational waves?
• RQ3 Can the gravitational lepto/baryogenesis operator ∂μRjμ/M², generated at two-loop level, efficiently produce lepton asymmetry under a stiff equation of state (ω > 1/3)?
• RQ4 To what extent can a combination of gravitational wave signals and neutrinoless double beta decay experiments constrain the mass scale of the lightest right-handed neutrino and the onset of radiation domination?
• RQ5 How do the spectral shape and amplitude of GWs from cosmic strings depend on the post-inflationary equation of state and string tension?

Key findings

• A gravitational wave spectrum with a flat plateau followed by a rising amplitude at high frequencies is a signature of a stiff post-inflationary equation of state (ω > 1/3), such as kination, in the pre-BBN era.
• The rising GW amplitude is correlated with enhanced lepton asymmetry production via the gravitational operator ∂μRjμ/M², which is proportional to (1−3ω), making ω > 1/3 a necessary condition for efficient asymmetry generation.
• The final baryon asymmetry is predicted by the master formula NfB−L ≈ (κβ)/(8zin⁸) × exp(−4K₁/z∗), which matches numerical solutions with high accuracy.
• For ω = 1 (kination), the frozen-out asymmetry scales as NG0B−L ∝ β/κ, and the washout factor is e−∫WIDdz ≈ exp(−4K₁/z∗), with K₁ being the modified Bessel function.
• A detectable GW amplitude with Gμ ≲ 10⁻¹² and a spectral break followed by a rise can be probed by LISA and future PTAs, especially when combined with a signal in neutrinoless double beta decay experiments.
• The model predicts that the lightest right-handed neutrino mass scale can be constrained to the intermediate scale (e.g., M₁ ≳ 10⁸ GeV) if both GW and double beta decay signals are observed.