Loop Corrections to Scalar Quintessence Potentials

Observations indicate that dark energy constitutes a substantial fraction of our Universe [1, 2, 3, 4, 5]. The range of possible candidates includes a cosmological constant and more flexible some form of dark energy with time dependent equation of state, called quintessence [6]. Commonly, realizations of quintessence scenarios feature a light scalar field [7, 8, 9]. The evolution of the scalar field is usually treated at the classical level. However, quantum fluctuations may alter the classical quintessence potential. In this article, we will investigate one-loop contributions both from quintessence and fermion fluctuations to the effective potential. We will show that in the late universe, quintessence fluctuations are harmless for most of the potentials used in the literature. For inverse power laws and SUGRA inspired models, this has already been demonstrated in [10]. On the other hand, we will demonstrate that fermion fluctuations severely restrict the magnitude of a possible coupling of quintessence to fermionic dark matter. In Euclidean conventions, the action we use for the quintessence field Φ and a fermionic species Ψ to which it may couple [11, 12, 13] is