Primordial and asymptotic inflation in Brans-Dicke cosmology

We show that rapid primordial inflation and slow asymptotic inflation is a natural consequence of Brans-Dicke theory. The ratio of the two inflation parameters is proportional to the square root of the Brans-Dicke parameter ω (ω ≫ 1). We also calculate the Hubble parameter H and the time variation of the time dependent Newtonian gravitational constant G for both regimes. The variation of the Hubble parameter predicted by Brans-Dicke cosmology is shown to be consistent with recent measurements. The inflationary universe model whose key feature is a finite period of primordial rapid exponential expansion has been proposed to resolve a number of cosmological puzzles, including the horizon, flatness and monopole problems. In the original or ‘old inflation model’ [1], the universe supercools into a false vacuum phase and its energy density acts as an effective cosmological constant which causes an epoch of de-Sitter (exponential) expansion. In this old inflation model, the de-Sitter expansion never ends and for a generic first order phase transition, there appears an energy barrier between the false vacuum and the true vacuum phases. This problem is known as the ‘graceful exit’ problem. In the extended inflation [2] model, on the other hand, the spirit of the old inflation model is conserved in the sense that the universe undergoes a generic, strongly first order phase transition associated with some (unspecified) high temperature particle physics phenomenon (e.g., gauge symmetry braking). As in the old inflation model, the energy scale for the transition can be much lower than the Planck scale so that quantum gravity effects can be ignored. In our work, we start up with a strong link between inflation and Brans-Dicke [3] theory of gravity. The theory is parameterized by a dimensionless constant ω, where ω → ∞ as Brans-Dicke theory goes over to the Einstein theory [4]. Present limits of the constant ω based on time-delay [5] experiments require ω > 500 ≫ 1. We assume that the scalar potential is composed only of the scalar field mass term and that φ evolves with time. The proposed model in this work is simple in that no other phenomenon such as the domination of the false vacuum over the scalar field energy density as in the extended inflation