AffleckDine

The Affleck-Dine mechanism is a theoretical framework in cosmology and particle physics for generating the baryon asymmetry of the universe within supersymmetric theories. Proposed by Ian Affleck and Michael Dine in 1985, it uses scalar fields associated with flat directions of the supersymmetric potential that carry baryon and/or lepton number.

In the early universe, particularly during or after inflation, a complex scalar field phi along a flat direction acquires a large vacuum expectation value. Soft supersymmetry-breaking terms and nonrenormalizable operators lift the flat direction, while baryon-number–violating (and CP-violating) A-terms induce a rotation in phi's complex plane. As the Hubble rate drops to around the mass scale of the field, the condensate begins coherent oscillations, and the rotating phase generates a net baryon number. The decay or fragmentation of this condensate transfers the asymmetry to standard model particles, yielding the observed baryon asymmetry.

In some potentials the condensate fragments into non-topological solitons called Q-balls, which can alter the relic abundance and decay history. The mechanism also accommodates leptogenesis by choosing flat directions carrying lepton number.

Affleck-Dine baryogenesis is a leading candidate in SUSY-based cosmologies, linking high-energy theory with early-universe dynamics. It interacts with constraints from reheating and isocurvature perturbations and has various model realizations depending on the MSSM field content and the form of nonrenormalizable operators.