  The present work deals with the cosmological consequences of the variable
cosmological term $\Lambda(a)=\Lambda_0 + \Lambda_1 a^{-r} + \Lambda_2 a^{-s},$
where $a$ is the scale factor of the Robertson-Walker space-time. An analysis
of the parameters $\Lambda_1,\Lambda_2,r,s$ and $\alpha,$ which describes the
interaction between the cosmological constant and non-relativistic
matter/radiation, leads to an attractive density $\rho_{\text{dm}} \sim a^{-r}$
and a repulsive density $\rho_{\text{infl}} \sim a^{-s}.$ As already known from
literature, an approach of the form $\Lambda(a)=\Lambda_0 + \Lambda_1 a^{-r}$
and the identification of the energy density of space-time expansion with the
zero-point density can avoid the scale discrepancy of the cosmological constant
problem and solve the missing mass problem of dark matter. Furthermore, this
works demonstrates that the additional term $\Lambda_2 a^{-s}$ solves the
flatness, the horizon and the magnetic-monopole problem without a hypothetical
scalar field, which avoids speculations about the origin of this field. As a
consequence, the imaginary time concept from Hartle and Hawking appears
naturally.
