On Nonrelativistic Isotropic and Homogeneous Universe

TL;DR

This paper develops a nonrelativistic cosmological model within a five-dimensional Galilean framework, deriving solutions that resemble standard cosmology and connecting to Milne's universe, offering an alternative to relativistic models.

Contribution

It introduces a novel nonrelativistic cosmological model based on Galilean covariance with solutions analogous to relativistic cosmology, including a connection to Milne's universe.

Findings

Derived two solutions: vacuum with exponential-quadratic scale factor and dust-dominated universe.

Model reproduces Milne's Newtonian cosmology under zero spatial curvature.

Framework aligns with Planck data on near-zero spatial curvature.

Abstract

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 ($\lambda=0$) yielding an exponential--quadratic scale factor, and (ii) a dust-dominated universe ($\lambda=1$) 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.