[Paper Review] The B-L Phase Transition: Implications for Cosmology and Neutrinos

Kai Schmitz|arXiv (Cornell University)|Jul 15, 2013

Cosmology and Gravitation Theories234 references11 citations

TL;DR

This paper proposes that the $B$-$L$ phase transition in the early universe triggers hybrid inflation, leading to tachyonic preheating, cosmic string formation, and the production of heavy (s)neutrinos that drive reheating, generate baryon asymmetry, and enable thermal gravitino production. A key result is a lower bound of $10\,\text{GeV}$ on the gravitino mass when consistent with leptogenesis and gravitino dark matter, with alternative non-thermal WIMP dark matter possible via heavy gravitino decay.

ABSTRACT

We investigate the possibility that the hot thermal phase of the early universe is ignited in consequence of the B-L phase transition, which represents the cosmological realization of the spontaneous breaking of the Abelian gauge symmetry associated with B-L, the difference between baryon number B and lepton number L. Prior to the B-L phase transition, the universe experiences a stage of hybrid inflation. Towards the end of inflation, the false vacuum of unbroken B-L decays, which entails tachyonic preheating as well as the production of cosmic strings. The dynamics of the B-L breaking Higgs field and the B-L gauge degrees of freedom, in combination with thermal processes, generate an abundance of heavy (s)neutrinos. These (s)neutrinos decay into radiation, thereby reheating the universe, generating the baryon asymmetry of the universe and setting the stage for the thermal production of gravitinos. We study the B-L phase transition in the full supersymmetric Abelian Higgs model, for which we derive and discuss the Lagrangian in arbitrary and unitary gauge. As for the subsequent reheating process, we formulate the complete set of Boltzmann equations, the solutions of which enable us to give a detailed and time-resolved description of reheating. Assuming the gravitino to be the lightest superparticle (LSP), the requirement of consistency between hybrid inflation, leptogenesis and gravitino dark matter implies relations between neutrino and superparticle masses, in particular a lower bound on the gravitino mass of 10 GeV. Similarly, in the case of very heavy gravitinos, the nonthermal production of pure wino or higgsino LSPs in heavy gravitino decays can account for the observed amount of dark matter, while simultaneously fulfilling the constraints imposed by primordial nucleosynthesis and leptogenesis.

Motivation & Objective

• To explore the cosmological implications of the $B$-$L$ phase transition as a mechanism for initiating the hot early universe.
• To investigate how $B$-$L$ breaking generates heavy (s)neutrinos that drive reheating and produce the baryon asymmetry via leptogenesis.
• To derive constraints on neutrino parameters and superparticle masses when the gravitino is the lightest supersymmetric particle (LSP).
• To examine alternative dark matter scenarios involving non-thermal production of pure wino or higgsino LSPs from heavy gravitino decays.
• To constrain undetermined neutrino observables using a Froggatt-Nielsen flavor structure within the seesaw mechanism.

Proposed method

• Formulate the full supersymmetric Abelian Higgs model Lagrangian in both arbitrary and unitary gauge to describe the $B$-$L$ phase transition.
• Derive and solve a complete set of Boltzmann equations to model time-resolved evolution of particle abundances during reheating.
• Use the seesaw mechanism with Froggatt-Nielsen flavor structure to relate heavy right-handed neutrino masses to light neutrino masses.
• Compute reheating temperature $T_{\text{RH}}$ as a function of $\widetilde{m}_1$ and $M_1$, linking it to the baryon asymmetry via $\eta_B \propto \widetilde{m}_1 / M_1$.
• Analyze gravitino abundance $\Omega_{\widetilde{G}} h^2$ as a function of $m_{\widetilde{G}}$, $m_{\tilde{g}}$, and $T_{\text{RH}}$, solving for constant abundance under varying gluino mass.
• Derive a quadratic equation for rescaled gravitino mass $m_{\widetilde{G}}$ to maintain constant dark matter abundance across different gluino masses.

Experimental results

Research questions

• RQ1 Can the $B$-$L$ phase transition serve as the origin of the hot thermal phase in the early universe, consistent with inflation and reheating?
• RQ2 What constraints arise on neutrino parameters and superparticle masses when the gravitino is the LSP and must simultaneously satisfy leptogenesis and dark matter constraints?
• RQ3 Can non-thermal production of pure wino or higgsino LSPs from heavy gravitino decays account for the observed dark matter abundance without violating nucleosynthesis or leptogenesis bounds?
• RQ4 How does the inclusion of a Froggatt-Nielsen flavor structure in the seesaw model constrain previously unknown neutrino observables?
• RQ5 What is the functional dependence of the rescaled gravitino mass on the gluino mass and original gravitino mass to preserve constant dark matter abundance?

Key findings

• The $B$-$L$ phase transition at the grand unification scale generates tachyonic preheating and cosmic strings, providing a dynamical origin for the hot early universe.
• Heavy (s)neutrinos produced during the transition decay into radiation, driving reheating and generating the baryon asymmetry via leptogenesis.
• A lower bound of $10\,\text{GeV}$ on the gravitino mass is required to maintain consistency between hybrid inflation, leptogenesis, and gravitino dark matter.
• For $m_{\widetilde{G}}^{0} \lesssim 280\,\text{GeV}$, the rescaled gravitino mass $m_{\widetilde{G}}^{-}$ is closer to the original mass, while for $m_{\widetilde{G}}^{0} \gtrsim 280\,\text{GeV}$, $m_{\widetilde{G}}^{+}$ dominates.
• Non-thermal production of pure wino or higgsino LSPs from heavy gravitino decays can account for the observed dark matter density while satisfying primordial nucleosynthesis and leptogenesis constraints.
• The rescaled gravitino mass follows a quadratic solution $m_{\widetilde{G}}^{\pm}$, with $m_{\widetilde{G}}^{0} \simeq 280\,\text{GeV}$ marking the point where helicity $\pm\frac{1}{2}$ and $\pm\frac{3}{2}$ states contribute equally to the abundance.