The particle horizon represents the boundary between observable and unobservable regions of the universe, which changes as the universe expands. Based on transformation optics, hyperbolic electromagnetic metamaterials can be utilized to simulate metrics with different signs due to their unique anisotropic properties. In this paper, we use hyperbolic metamaterials to visually depict the variation of the particle horizon under three models of an expanding universe (open, flat, and closed) by substituting one-dimensional time with one-dimensional space. The good agreement between theory and simulation confirms that hyperbolic metamaterials are excellent for simulating space-times, suggesting their potential as a new platform for cosmological analogies.