# Classical de Sitter Solutions of Ten-Dimensional Supergravity

## TL;DR

This paper constructs explicit ten-dimensional supergravity solutions that yield four-dimensional de Sitter space, involving localized orientifold planes and negative curvature internal spaces, with potential implications for string cosmology.

## Contribution

It provides the first explicit ten-dimensional supergravity solutions with localized orientifolds leading to de Sitter compactifications, including detailed backreaction analysis.

## Key findings

- Solutions are numerical but with analytically verified orientifold charge and tension.
- Internal space topology includes a circle times an Einstein manifold of negative curvature.
- Solutions are moduli-stable at tree level and can be weakly coupled and curved.

## Abstract

We find four-dimensional de Sitter compactifications of type IIA supergravity by directly solving the ten-dimensional equations of motion. In the simplest examples, the internal space has the topology of a circle times an Einstein manifold of negative curvature. An orientifold acts on the circle with two fixed loci, at which an O8$_-$ and an O8$_+$ plane sit. These orientifold planes are fully backreacted and localized. While the solutions are numerical, the charge and tension of the orientifold planes can be verified analytically. Our solutions have moduli at tree level and can be made parametrically weakly-coupled and weakly-curved. Their fate in string theory depends on quantum corrections.