Weak gravity conjecture in the asymptotical dS and AdS background

TL;DR

This paper explores the weak gravity conjecture in asymptotic de Sitter and anti-de Sitter spaces, deriving bounds on gauge couplings and cosmological constants, and connecting these to string theory and de Sitter entropy.

Contribution

It generalizes the weak gravity conjecture to asymptotic dS and AdS spaces, providing bounds on gauge couplings and insights into de Sitter entropy within string theory.

Findings

Lower bound on U(1) gauge coupling in dS space

Upper bound on cosmological constant for gauge theory survival

Extension of results to U(N) gauge theories and AdS space

Abstract

The cosmological observations provide a strong evidence that there is a positive cosmological constant in our universe and thus the spacetime is asymptotical de Sitter space. The conjecture of gravity as the weakest force in the asymptotical dS space leads to a lower bound on the U(1) gauge coupling $g$, or equivalently, the positive cosmological constant gets an upper bound $\rho_V \leq g^2 M_p^4$ in order that the U(1) gauge theory can survive in four dimensions. This result has a simple explanation in string theory, i.e. the string scale $\sqrt{\alpha '}$ should not be greater than the size of the cosmic horizon. Our proposal in string theory can be generalized to U(N) gauge theory and gives a guideline to the microscopic explanation of the de Sitter entropy. The similar results are also obtained in the asymptotical anti-de Sitter space.