  Suppose that the early Universe starts with a quantum spacetime originated
cosmological $\Lambda$-term at the Planck scale $M_{\rm pl}$. The cosmological
energy density $\rho_{_{_\Lambda}}$ drives inflation and simultaneously reduces
its value to create the matter-energy density $\rho_{_{_M}}$ via the continuous
pair productions of massive fermions and antifermions. The decreasing
$\rho_{_{_\Lambda}}$ and increasing $\rho_{_{_M}}$, in turn, slows down the
inflation to its end when the pair production rate $\Gamma_M$ is larger than
the Hubble rate $H$. The density $\rho_{_{_\Lambda}}$ and Hubble rate $H$ are
uniquely determined by two independent equations from the Einstein equation and
energy conservation law, besides the $\rho_{_{_M}}$ is determined by pair
productions. As a result, inflation naturally appears and theoretical results
agree with Planck 2018 observations. Suppose that the reheating efficiently
converts $\rho_{_{_\Lambda}}$ to $\rho_{_{_M}}\gg \rho_{_{_\Lambda}}$
accounting for the most relevant Universe mass, and some massive pairs decay to
relativistic particles of energy density $\rho_{_{_R}}$ starting the hot Big
Bang. The back reaction $\rho_{_{_M}}\leftrightarrow H\leftrightarrow
\rho_{_{_\Lambda}}$ is weak but continues. As a consequence, $\rho_{_\Lambda}$
closely tracks down $\rho_{_R}$ from the reheating end up to the
radiation-matter equilibrium, then it varies very slowly,
$\rho_{_\Lambda}\propto$ constant, due to the transition from radiation
dominant epoch to matter dominant epoch. Therefore the cosmic coincidence
problem can be possibly avoided.
