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Register a new userCosmological $Lambda$ driven inflation and produced massive particles
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She-Sheng Xue
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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 $rho_{_{_M}}leftrightarrow Hleftrightarrow rho_{_{_Lambda}}$ 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.
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A novel scalar field free approach to cosmic inflation is presented. The inflationary Universe and the radiation dominated Universe are shown, within the framework of unified brane cosmology, to be two different phases governed by one and the same energy density. The phase transition of second order (the Hubble constant exhibits a finite jump) appears naturally and serves as the exit mechanism. No re-heating is needed. The required number of e-folds is achieved without fine tuning.
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.
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