Multidimensional Topological Foam

TL;DR

This paper analyzes a multidimensional cosmological model with complex topology, showing that its equations simplify to depend only on effective curvatures and dimensions, and relates its effective action to that of a bosonic string.

Contribution

It demonstrates exact solutions for the equations of motion and establishes a connection between the model's effective action and bosonic string theory.

Findings

Equations depend only on effective curvatures and dimensions.

Exact solutions are obtainable despite complex topology.

Effective action matches that of a bosonic string in certain cases.

Abstract

Multidimensional cosmological model with the topology M=RxM_1xM_2x...xM_n where M_i (i=1,... ,n) undergo a chain splitting into arbitrary number of compact spaces is considered. It is shown that equations of motion can be solved exactly because they depend only on the effective curvatures and dimensions and "forget" about inner topological structure. It is proved that effective cosmological action for the model with n=1 in the case of infinite splitting of the internal space coincides with the tree-level effective action for a bosonic string.