Building Supergravity Quintessence Model

TL;DR

This work investigates how to realize quintessence within supergravity under swampland constraints, focusing on the tension that SUSY breaking induces a gravitino-scale mass for the quintessence field. It develops two distinct strategies: (i) a shift-symmetric quintessence sector that allows embedding arbitrary potentials with suppressed fifth-force effects, enabling possible $w>-1$ observations, and (ii) a sequestered supergravity setup that minimizes SUSY-breaking mediation to the quintessence sector, typically yielding small field displacements and $w$ very close to $-1$. For the shift-symmetric route, the quintessence potential is generated via a holomorphic superpotential $W_1(Q)$ (e.g., with $W_1(Q) = \Lambda^3 f(Q/M_{P\ell})$) and can accommodate a cosmological-constant-like late-time behavior while remaining radiatively stable; an SQCD axion example yields a cosine-type potential linked to the electroweak and Planck scales. In the sequestered scenario, the quintessence field remains largely decoupled from SUSY breaking at tree level, but fifth-force constraints force the field displacement to be tiny (e.g., $(\tilde Q/M_{P\ell})^2 \lesssim 10^{-5}$), making deviations of $w$ from $-1$ difficult to detect and potentially clashing with the swampland bound unless the slope parameter is parametrically small. The results delineate the trade-offs between theoretical consistency and observational signatures in SUGRA quintessence models.

Abstract

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 $c \ll 1$.

Figures (1)

• Figure 1: (Left): Plot of the quintessence potential Eq.(\ref{['GeneralQV']}) with the given parameters. The potential has an inflection point at $q=0.60024$. The parameters are chosen in a way such that at the global minimum has $V=0$, while the quintessence field contributes the right amount of energy when it slow rolls on the plateau. (Right): The evolution of the equation of state parameter $w$ for the potential shown in the left panel with various initial conditions, in comparison with the $w(z)$ given in Ade:2015rim which was reconstructed from observational data. We see that, for instance, with the quintessence field starting at $q_i=4.5$, one can have a interesting deviation from $w=-1$ that still satisfies current constraints.