  We explore the cosmological model in which a late-time mild inflation is
realized after the star formation epoch. Non-vanishing curvature coupling of a
classical boson field yields this mild inflation without a cosmological
constant. Accordingly the lifetime of the present Universe is remarkably
increased in our model. Thus we show that the present observed high value of
the Hubble parameter $H_0 \approx 70-80{\rm km/sec/Mpc}$ is compatible with the
age of the oldest stars $14{\rm Gyr}$ without introducing the cosmological
constant or the open Universe model. Moreover in our model, the local Hubble
parameter becomes larger than the global one. Thus we show that the present
observed local Hubble parameter measured by using the Cepheid variables is
compatible with the global Hubble parameter measured by using the
Sunyaev-Zeldovich effect. We also examine the energy conditions, evolution of
the effective gravitational constant and the nucleosynthesis process.
