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We study the classical Friedman equations for the time-varying cosmologicalterm $\tilde\Lambda$ and Hubble function $H$, together with quantised fieldequations for the production of massive $M\gg H$ particles, namely, the$\tilde\Lambda$CDM scenario of dark energy and matter interactions. Classicalslow components ${\mathcal O}(H^{-1})$ are separated from quantum fastcomponents ${\mathcal O}(M^{-1})$. The former obeys the Friedman equations, andthe latter obeys a set of nonlinear differential equations. Numerically solvingequations for quantum fast components, we find the production and oscillationof massive particle-antiparticle pairs in microscopic time scale ${\mathcalO}(M^{-1})$. Their density and pressure averages over microscopic time do notvanish. It implies the formation of a massive pair plasma state in macroscopictime scale ${\mathcal O}(H^{-1})$, whose effective density and pressurecontribute to the Friedman equations. Considering the inflation driven by thetime-varying cosmological term and slowed down by the massive pair plasmastate, we obtain the relation of spectral index and tensor-to-scalar ratio inagreement with recent observations. We discuss the singularity-freepre-inflation, the CMB large-scale anomaly, and dark-matter densityperturbations imprinting on power spectra.

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