Weak gravity conjecture in the asymptotical dS and AdS background

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 ${\rho }_V\le g^2{M}_p^4$ 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 $\sqrt{{\alpha }^{\prime }}$ 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.

4 pages; version for publication in JHEP (title changed)

References in corpus (1)

• Some Low Dimensional Evidence for the Weak Gravity Conjecture

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