Cosmological $Lambda$ converts to reheating energy and cold dark matter

The cosmological energy density $rho_{_{_Lambda}}$ at the Planck scale $M_{rm pl}$ drives inflation and simultaneously reduces its value to create the pair-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 $H$ of inflation. A large number of massive pairs is produced and reheating epoch starts. In addition to the Einstein equation and energy-conservation law, we introduce the Boltzmann-type rate equation describing the number of pairs produced from (annihilating to) the spacetime, and reheating equation describing massive unstable pairs decay to relativistic particles and thermodynamic laws. This forms a close set of four independent differential equations uniquely determining $H$, $rho_{_Lambda}$, $rho_{_M}$ and radiation-energy density $rho_{_R}$, given the initial conditions at inflation end. Numerical solutions demonstrate three episodes of preheating, massive pairs dominate and genuine reheating. Results show that $rho_{_Lambda}$ can efficiently convert to $rho_{_M}$ by producing massive pairs, whose decay accounts for reheating $rho_{_R}$, temperature and entropy of the Big-Bang Universe. The stable massive pairs instead account for cold dark matter. Using CMB and baryon number-to-entropy ratio measurements, we constrain the effective mass of pairs, Yukawa coupling and degeneracies of relativistic particles. As a result, the obtained inflation $e$-folding number, reheating scale, temperature and entropy are in terms of the tensor-to-scalar ratio in the theoretically predicated range $0.042lesssim r lesssim 0.048$, consistently with current observations.