The Helium Abundance Problem and Non-minimally Coupled Quintessence

Recently, it has been discovered that the expansion of the Universe is accelerating. This requires the existence of a dark energy component in the Universe with an equation of state p = wρ, w < 0. One example of such a component is a cosmological constant. However, it is difficult to understand in the present framework of particle physics why it is so small. A fine tuning of 10 is required if the cosmological constant arises from Planck scale physics. Quintessence models were suggested as an alternative to cosmological constant. In quintessence models, a scalar field provides the dark energy which drives the accelerated expansion of the Universe. The evolution of the scalar field is such that its equation of state mimics the dominant component of the Universe, thus explains why it is so small at present time. In Non-minimally Coupled (NMC) quintessence models the scalar field couples to the gravitational constant. The action of NMC can be written as