The metric that models a homogeneous and isotropic universe in general relativity is the FLRW metric.
FLRW stands for Friedmann–Lemaître–Robertson–Walker, honoring Alexander Friedmann, Georges Lemaître, Howard Robertson, and Arthur Walker. The metric assumes that, on sufficiently large scales, space looks the same at every location and in every direction. These are the cosmological principles of homogeneity and isotropy.
Its central time-dependent quantity is the scale factor, usually written a(t). This factor describes how distances between comoving galaxies change as the universe expands or contracts. The spatial geometry may be flat, positively curved, or negatively curved, corresponding to different values of the spatial-curvature parameter.
The metric itself is a geometric framework, not a complete prediction of cosmic history. Combining it with the Einstein field equations and a model for matter, radiation, and dark energy yields the Friedmann equations. Those equations underpin modern cosmology and the Lambda-CDM model.
The other options describe specific settings: Minkowski space is flat and non-expanding, while Kerr and Reissner–Nordström metrics model rotating or charged black holes.