  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 NEC
and is stable. Upon turning on gravity, this model describes the early Genesis
stage.
