N=2 Gauged Supergravity with Stable dS Vacuum and Masses of Ultra-Light Scalars in Einstein Field Equations
In most of the models of dark energy it is assumed that the cosmological constant is equal to zero and the potential energy V (φ) of the scalar field driving the present stage of acceleration, slowly decreases and eventually vanishes as the field rolls to φ = ∞. In this case, after a transient dS-like stage, the speed of expansion of the Universe decreases, and the Universe reaches Minkowski regime. Recently, it was found that one can describe dark energy in some d = 4 extended supergravities that have dS solutions. These dS solutions correspond to the extrema of the effective potential V (φ) for some scalar fields φ. In this paper, we introduce a non-minimal coupling between the scalar curvature and the density of a scalar in the form L = −ξ√gRφ∗φ = −ξR̃φ∗φ, ξ = 1 6 and we consider a complex potential in the form V (φφ∗) = pm(1 − ωφφ) where p is a constant of order of unity, φ∗ is a complex field and ω is a parameter assumed to be ≪ 1. It was shown that the mass squared of the scalar field is quantized in units of the cosmological constant as m = nΛ, where n are some integers in agreement with N = 2 gauged supergravity with stable dS vacuum. We show that this result could have important consequences on dark energy problem. We discuss some important consequences on standard cosmology withouit violating any of the well-known test of General Relativity. I-Introduction It is well believed today that the cosmological constant describes the energy density of the vacuum (empty space), and it is a potentially important contributor to the dynamical history of the Universe. Recent observations of Type Ia supernovae and the CMB indicates that the Universe is in accelerated regime [1]. The total energy of the universe consists in fact of ordinary matter and dark matter. One can interpret the dark energy as the vacuum energy corresponding to the cosmological Einstein constant or as the slowly changing energy of a certain scalar field