We investigate the inflationary consequences of the oscillating dark energy model proposed by Tián [Phys. Rev. D 101, 063531 (2020)], which aims to solve the cosmological coincidence problem with multi-accelerating Universe (MAU). We point out that the inflationary dynamics belong to slow-roll inflation. The spectral index of scalar perturbations and the tensor-to-scalar ratio r are shown to be consistent with current Planck measurements. Especially, this model predicts r ∼ 10 −7 , which is far below the observation limits. This result motivates us to explore the smallness of r in the general MAU. We propose a quintessential generalization of the original model and prove r < 0.01 in general. The null detection to date of primordial gravitational waves provides a circumstantial evidence for the MAU. After the end of inflation, the scalar field rolls toward infinity instead of a local minimum, and meanwhile its equation of state is oscillating with an average value larger than 1/3. In this framework, we show that gravitational particle creation at the end of inflation is capable of reheating the Universe.