On Nonrelativistic Isotropic and Homogeneous Universe

This article deals with a nonrelativistic cosmological model based on Galilean covariance, formulated within a five-dimensional Galilean manifold. Within this framework, we construct an isotropic and homogeneous metric analogous to the Friedmann–Robertson–Walker metric but without a universal speed limit. Two distinct solutions of the Einstein-like field equations are obtained: (i) a vacuum configuration (λ = 0) yielding an exponential.quadratic scale factor, and (ii) a dustdominated universe (λ = 1) described by a non-interacting nonrelativistic fluid. Upon dimensional reduction to 3+1 spacetime through a specific embedding, the model naturally develops anisotropy in the scale factor and density, consistent with the near-zero spatial curvature inferred from Planck data. In the case of vanishing spatial curvature, the framework reproduces Milne’s Newtonian cosmology because this condition leads to a vanishing pressure. This provides an independent nonrelativistic setting for cosmological dynamics within Galilean covariance.