Inflation and Transition to a Slowly Accelerating Phase from S.S.B. of Scale Invariance

TL;DR

This paper explores how adding an $R^2$ term to a scale-invariant model leads to a transition from an inflationary phase to a slowly accelerating universe, explaining the small vacuum energy observed today.

Contribution

It introduces a scale-invariant model with an $R^2$ term that naturally produces a potential with two flat regions, linking inflation and current acceleration.

Findings

A non-trivial dilaton potential with two flat regions is generated.

The model explains the small vacuum energy via a see-saw mechanism.

Transition from inflation to a slowly accelerating universe is achieved.

Abstract

We consider the effects of adding a scale invariant $R^{2}$ term to the action of the scale invariant model (SIM) studied previously by one of us (E.I.G., Mod. Phys. Lett. A14, 1043 (1999)). The SIM belongs to the general class of theories, where an integration measure independent of the metric is introduced. To implement scale invariance (S.I.), a dilaton field is introduced. The integration of the equations of motion associated with the new measure gives rise to the spontaneous symmetry breaking (S.S.B) of S.I.. After S.S.B. of S.I. in the model with the $R^{2}$ term, it is found that a non trivial potential for the dilaton is generated. This potential contains two flat regions: one associated with the Planck scale and with an inflationary phase, while the other flat region is associated to a very small vacuum energy (V.E.) and is associated to the present slowly accelerated phase of the universe (S.A.PH). The smallness of the V.E. in the S.A.PH. is understood through the see saw mechanism introduced in S.I.M.