Construction of matter models which violate the strong energy condition and may avoid the initial singularity

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Abstract
Lagrangians of matter models with interaction are constructed, which induce a violation of the strong energy condition. In particular, the usual interaction between fermions and scalar mesons Lint=g psi psi phi , is investigated in the mean-field approximation. The regions of parameters (coupling constant, masses of fermions and mesons) are given in which the strong energy condition is violated. With this matter model, cosmological Friedmann evolutions back in time are computed. The question of whether the initial singularity is avoidable in this context is of particular interest.