  The dynamics at the end of inflation can generate an asymmetry between
particles and anti-particles of the inflaton field. This asymmetry can be
transferred to baryons via decays, generating a baryon asymmetry in our
Universe. We explore this idea in detail for a complex inflaton governed by an
observationally consistent -"flatter than quadratic"- potential with a weakly
broken global U(1) symmetry. We find that most of the inflaton asymmetry is
locked in non-topological soliton like configurations (oscillons) produced
copiously at the end of inflation. These solitons eventually decay into baryons
and generate the observed matter-antimatter asymmetry for a range of model
parameters. Through a combination of three dimensional lattice simulations and
a detailed linearized analysis, we show how the inflaton asymmetry depends on
the fragmentation, the magnitude of the symmetry breaking term and initial
conditions at the end of inflation. We discuss the final decay into baryons,
but leave a detailed analysis of the inhomogeneous annihilation, reheating and
thermalization to future work.
  As part of our work, we pay particular attention to generating multifield
initial conditions for the field fluctuations (including metric perturbations)
at the end of inflation for lattice simulations.
