A multidimensional radiation-filled universe (Q1095431)

We consider a radiation-filled universe which possesses the product symmetry: (N-dimensional space of constant curvature) \(\times\) (n sphere). The solutions of all the types, within this class, to the classical field equations are given. In the case of the N-dimensional space of zero or negative curvature constant, the solutions exhibit a tendency to approach asymptotically the Kasner-like state in which the N- dimensional subspace expands while the n sphere shrinks to the final singularity. Our conclusions based on the phase-diagram method are in agreement with the results concerning the \({\mathbb{R}}^ N\times S^ n\) universe calculated by Sahdev with the help of numerical methods.