Massive particle pair production and oscillation in Friedman Universe: its effect on inflation

We study the classical Friedman equations for the time-varying cosmological term $\tilde\Lambda$ and Hubble function $H$, together with quantised field equations for the production of massive $M\gg H$ particles, namely, the $\tilde\Lambda$CDM scenario of dark energy and matter interactions. Classical slow components ${\mathcal O}(H^{-1})$ are separated from quantum fast components ${\mathcal O}(M^{-1})$. The former obeys the Friedman equations, and the latter obeys a set of nonlinear differential equations. Numerically solving equations for quantum fast components, we find the production and oscillation of massive particle-antiparticle pairs in microscopic time scale ${\mathcal O}(M^{-1})$. Their density and pressure averages over microscopic time do not vanish. It implies the formation of a massive pair plasma state in macroscopic time scale ${\mathcal O}(H^{-1})$, whose effective density and pressure contribute to the Friedman equations. Considering the inflation driven by the time-varying cosmological term and slowed down by the massive pair plasma state, we obtain the relation of spectral index and tensor-to-scalar ratio in agreement with recent observations. We discuss the singularity-free pre-inflation, the CMB large-scale anomaly, and dark-matter density perturbations imprinting on power spectra.