Building Supergravity Quintessence Model

It was recently pointed out that the cosmological constant (even metastable one) belongs to the so-called "swampland" and hence cannot be obtained as the low-energy limit of string theory that requires $|\nabla V| > c V$. If true, the dark energy needs to be described by an evolving scalar field, i.e., quintessence with $w>-1$ within supergravity. However, the large hierarchy between the supersymmetry breaking scale and the energy scale of dark energy imposes a challenge on building quintessence models in supergravity as the quintessence field typically acquires a mass of order the gravitino mass. We investigate two approaches to circumvent this obstacle. One is imposing shift symmetry to the quintessence sector, and we demonstrate any quintessence potential can be embedded into supergravity and the fifth force constraint gives little limit on quintessence field displacement, leading to possible observational signature $w>-1$. The structure is stable against quantum corrections. A particular example can address the cosmic coincidence problem. The other approach is sequestered supergravity, and the stability requirement strongly constrains the form of the Kahler potential and superpotential, and the quintessence field displacement is typically much smaller than Planck mass. In addition, to satisfy the fifth force constraint, the quintessence field displacement is further restricted in the sequestered case, requiring $c \ll 1$.