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

TL;DR

This paper investigates the instability of quintessence models under entropy and distance conjectures, revealing that accelerating backgrounds with horizons are unstable due to entropy growth constraints, linking swampland conjectures with entropy bounds.

Contribution

It demonstrates the instability conditions of quintessence models using covariant entropy bounds and connects these conditions with the trans-Planckian censorship and AdS distance conjectures.

Findings

Accelerating quintessence backgrounds with horizons are unstable.

Instability conditions align with the trans-Planckian censorship bound.

Scale separation is achievable when entropy growth rates are bounded.

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 accelerating background having the event horizon is unstable, and the instability condition as well as the lifetime of the unstable background is equivalent to the trans-Planckian censorship bound forbidding the classicalization of the trans-Planckian modes. 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.