A simple way to construct models with early cosmological Genesis epoch is to employ bosonic fields whose Lagrangians transform homogeneously under scaling transformation. We show that in these theories, for a range of parameters defining the Lagrangian, there exists a homogeneous power-law solution in flat space-time, whose energy density vanishes, while pressure is negative (power-law Genesis). We find the condition for the legitimacy of the classical field theory description of such a situation. We note that this condition does not hold for our earlier Genesis model with vector field. We construct another model with vector field and power-law background solution in flat space-time, which is legitimately treated within classical field theory, violates the Null Energy Condition (NEC) and is stable. Upon turning on gravity, this model describes the early Genesis stage.
A multisymplectic framework for classical field theory and the calculus of variations II: space + time decomposition