HIGH ENERGY PHYSICS AND QUINTESSENCE a

It is shown that any realistic model of quintessence should be based on Supergravity (SUGRA) since the value of the quintessence field on the attractor is approximately the Planck mass. Under very general assumptions, the typical shape of a SUGRA tracking potential is derived. Cosmological implications are investigated. In particular, it is demonstrated that, generically, the equation of state parameter is driven to a value close to −1 in agreement with recent observations. If confirmed, the discovery that our Universe is presently undergoing a phase of accelerated expansion 1 has clearly important implications for Cosmology and High Energy Physics. In particular, a crucial question is to identify the physical nature of the dark matter component responsible for this acceleration which would represent 70% of the matter content of the Universe. A natural candidate is obviously the cosmological constant. The cosmological constant energy density includes in fact contributions from two origins. The first contribution is due to the bared cosmological, Λ 0 , which appears in the Einstein equations as a " free parameter " and the second one is due to the zero-point fluctuations of the quantum fields. This gives rise to energy densities respectively equal to Λ 0 c 4 /(8πG) and (¯ hc/2) d 3 kk/(2π) 3 ≈ ¯ hck 4 max /(16π 2). In the last expression, k max is a cutoff which can naturally be taken as the Planck wavenumber. As a consequence, the second contribution becomes huge. Since the observed value is tiny (0.7 times the critical energy density ρ c), one needs to fine-tune very accurately the value of the bared constant Λ 0 such that the previous simple theoretical predictions be compatible with observational data. Let us emphasize that the discovery that the Universe is accelerating renders this problem even worse than before. Indeed, it is probably easier to explain why there is an exact cancellation between the two contributions such that ρ Λ = 0 (due, for example, to some