Late-Time Mild Inflation: A Possible Solution of a Dilemma: The Cosmic Age and the Hubble Parameter

Abstract

We explore the cosmological model in which a late-time mild inflation (LMI) is realized after the star formation epoch. Nonvanishing 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 this LMI model. Thus we show that the present observed high value of the Hubble parameter H0 ≈ 70–80 km/sec/Mpc is compatible with the age of the oldest stars 14 Gyr without introducing the cosmological constant or the dilute Universe model. Moreover in this LMI 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. Furthermore we examine several aspects of the LMI model: (a) The energy conditions are violated. We examine the consequences of these violations. (b) There is a natural evolution of the effective gravitational "constant" in high redshift region. This yields a drastic change of the stellar luminosity through the constructive equations of a star. We point out that a distant galaxy becomes much dimmer by this effect. (c) This varying gravitational "constant" affects the cosmic expansion speed and the nucleosynthesis process in the early Universe. We point out that this effect constrains the parameters of the LMI model though fine tuning is always possible.