1. Databases
2. Spacetime database
3. de Sitter

de Sitter

1. History

2. Topology

de Sitter space has the topology $\mathbb{R}\times S^{n-1}$.

3. Metrics and coordinates

Static coordinates

$$ds^2 = -(1 - \frac{1}{3} \Lambda r^2) dt^2 + \frac{1}{1 - \frac{1}{3} \Lambda r^2} dr^2 + r^2 (d\theta + \sin^2 \theta d\varphi^2)$$

Flat slicing coordinates

$$ds^2 = -d\tau^2 + e^{2\tau / \ell} (d\rho^2 + \rho^2 (d\theta + \sin^2 \theta d\varphi^2))$$

Open slicing

Closed slicing

Global coordinates

$$ds^2 = -d\tau + \ell^2 \cosh^2 (\frac \tau \ell) d\Omega_3^2$$

4. Tensor quantities

5. Symmetries

6. Stress-energy tensor

7. Curves

8. Equations

9. Causal structure

10. Asymptotic structure

11. Energy conditions

12. Limits and related spacetimes

13. Misc.

Bibliography