de Sitter in String Theory vs. Gibbons & Hawking

TL;DR

The paper demonstrates that perturbative string theory cannot support de Sitter spacetime solutions under certain assumptions, suggesting the universe may not evolve towards a de Sitter phase.

Contribution

It provides a proof that perturbative string theory does not admit de Sitter solutions to all orders, based on the behavior of the Euclidean quantum gravity partition function.

Findings

Perturbative string theory's effective action vanishes for closed Euclidean solutions.

The assumption about the sphere partition function relates to the Gibbons-Hawking entropy.

De Sitter solutions are incompatible with the string theory framework under these conditions.

Abstract

This paper corroborates a statement that perturbative string theory does not admit a solution whose spacetime metric is de Sitter times a closed manifold, to all orders in the $\alpha'$ and $g_s$ expansions, under the assumption that the logarithm of the sphere partition function of Euclidean quantum gravity receives a nonzero contribution proportional to $\frac{1}{G_N}$ in a saddle-point approximation. This assumption is related to the Gibbons-Hawking proposal that the entropy of the cosmological horizon of the static patch is $\frac{A}{4G_N}$. Evidence for the statement comes from independent approaches to the effective action of string theory, all of which agree that the tree-level action vanishes for closed Euclidean target-space solutions. One possible implication is that the state of the Universe will depart from an asymptotically de Sitter spacetime.