An extension of the cosmological standard model with a bounded Hubble expansion rate

The possibility of having an extension of the cosmological standard model with a Hubble expansion rate $H$ constrained to a finite interval is considered. Two periods of accelerated expansion arise naturally when the Hubble expansion rate approaches to the two limiting values. The new description of the history of the universe is confronted with cosmological data and with several theoretical ideas going beyond the standard cosmological model.