FLRW
The Friedman-Lemaître-Robertson-Walker spacetime (or FLRW, or FRW)
1. History
2. Topology
The topology of FLRW spacetimes varies, it is usually taken as $\mathbb{R} \times \Sigma$, with $\Sigma$ being a quotient of either $S^{n-1}$ (for positive curvature), $H^{n-1}$ (for negative curvature) or $\mathbb{R}^{n-1}$ (for zero curvature).
3. Metrics and coordinates
Standard coordinates
$$ds^2 = -dt^2 + a(t) \left[ \sum_i (dx^i)^2 \right]$$Conformal coordinates
$$ds^2 = \alpha(\eta) \left[ -d\eta^2 + \sum_i (dx^i)^2 \right]$$4. Tensor quantities
5. Symmetries
6. Stress-energy tensor
7. Curves
8. Equations
In conformal coordinates
$$u_k(x) = \frac{1}{(2\pi)^{(1-n) / 2}} e^{i \vec{k} \cdot \vec{x}} C^{(2 - n) / 4} \chi_k(\eta)$$ $$\frac{d^2 \chi_k}{d\eta^2} + \left\{ k^2 + C(\eta) \left[ m^2 + (\xi - \xi(n)) R(\eta) \right] \right\} \chi_k = 0$$9. Causal structure
The FLRW spacetime is globally hyperbolic.