Cosmological $\Lambda$ driven inflation and produced particles.

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, in addition, the $\rho_{_{_M}}$ is determined by pair productions. As a result, inflation naturally appears and theoretical results agree to 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 dominate to matter dominate epoch. Therefore the cosmic coincidence problem can be possibly avoided.