Background instability of quintessence model in light of entropy and distance conjecture

Abstract

We apply the covariant entropy bound argument supporting the de Sitter swampland conjecture to the quintessence model, to find out the condition for the background to be unstable. More concretely, the background is unstable when the matter entropy given by the species number of the effective field theory increases more rapidly than the geometrical entropy proportional to the apparent horizon area, since it contradicts the covariant entropy bound. The rapid increase in the matter entropy is proposed by the distance conjecture, which states that the time evolution of some scalar field along the geodesic in the field space brings about the descent of a tower of states from UV. From this, we find that for the quintessence model, the unstable background admits the event horizon of finite size, and the converse is also true when the string tower is taken into account. Here, the presence of the event horizon implies that the trans-Planckian modes can be classicalized, violating the trans-Planckian censorship bound. We also point out that the scale separation between the Kaluza-Klein mass scale and the Hubble parameter can be realized when the product between the increasing rates of the matter and the geometrical entropies is bounded from below, which is consistent with the AdS distance conjecture. Our study suggests that various swampland conjectures can be comprehensively understood in the language of the entropy.