| Summary: | Abstract We study the classical Friedman equations for the time-varying cosmological term $$\tilde{\Lambda }$$ Λ ~ and Hubble function H, together with quantised field equations for the production of massive $$M\gg H$$ M ≫ H particles, namely, the $$\tilde{\Lambda }$$ Λ ~ CDM scenario of dark energy and matter interactions. Classical slow components $${\mathcal O}(H^{-1})$$ O ( H - 1 ) are separated from quantum fast components $${\mathcal O}(M^{-1})$$ 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 $${\mathcal O}(M^{-1})$$ 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 $${\mathcal O}(H^{-1})$$ 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.
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