The entropic quasi-de Sitter instability time from the distance conjecture

TL;DR

This paper derives an entropic instability time for quasi-de Sitter spacetime based on the swampland conjectures, revealing a logarithmic factor that influences the spacetime's lifetime and related bounds.

Contribution

It introduces a new entropic instability time formula for quasi-dS spacetime incorporating the distance conjecture and entropy considerations, with a logarithmic enhancement.

Findings

The instability time depends on the slow-roll parameter and Hubble scale.

A logarithmic factor $ ext{log}(m_{Pl}/H)$ appears, affecting the geodesic distance.

Potential relaxation of bounds on the scalar potential's second derivative.

Abstract

From the entropy argument for the dS swampland conjecture which connects the Gibbons-Hawking entropy bound with the distance conjecture, we find the entropic quasi-dS instability time given by $1/(\sqrt{\epsilon_H}H)\log(m_{\rm Pl}/H)$ as the lifetime of quasi-dS spacetime. It depends on the slow-roll parameter, and contains the logarithmic factor $\log(m_{\rm Pl}/H)$ which can be found in the scrambling (or decoherence) time as well. Such a logarithmic factor enhances the geodesic distance of the modulus from the mere Planck scale, and also possibly relaxes the bound on $m_{\rm Pl}^2 \nabla^2 V/V$.