Non-Markovian Electroweak Baryogenesis: Memory Effects on CP-Violating Transport and Gravitational Waves

Abstract: We develop a non-Markovian extension of electroweak baryogenesis within the Schwinger--Keldysh real-time effective field theory framework and the Kadanoff--Baym hierarchy. When the relaxation time of CP-violating mediators becomes comparable to the bubble-wall crossing time, transport dynamics acquire temporal nonlocality, leading to memory-kernel corrections to the CP-violating source and diffusion equations beyond the Markovian approximation. These effects shift the optimal wall velocity to smaller values, narrow the viable parameter space, and induce a characteristic non-monotonic dependence of the baryon asymmetry on the memory timescale for sub-optimal wall velocities, which cannot be reproduced by a consistent Markovian reparameterisation. A systematic parameter analysis identifies regions compatible with the observed baryon asymmetry and constrains the allowed memory timescale from hydrodynamic stability and the physical range of the CP-violating phase. We also assess the correlated impact on the stochastic gravitational-wave signal, finding that memory effects can enhance the effective source duration and amplitude, although much of the viable parameter space remains below near-future detector sensitivities and theoretical uncertainties remain at the order-of-magnitude level. These results establish non-Markovian transport as a well-motivated extension of electroweak baryogenesis and introduce the memory timescale as a parameter testable through baryon asymmetry measurements, collider CP probes, and gravitational-wave observations.