Classification of multidimensional inflationary models

Details Classification of multidimensional inflationary models Classification of multidimensional inflationary models

1997-09-26

arxiv.org/abs/gr-qc/9709070v1

J.Math.Phys. 39 (1998) 998-1010

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

21 pages, LaTeX, no figures, J. Math. Phys. in print

Scientific paper

10.1063/1.532366

We define under which circumstances two multi-warped product spacetimes can be considered equivalent and then we classify the spaces of constant curvature in the Euclidean and Lorentzian signature. For dimension D=2, we get essentially twelve representations, for D=3 exactly eighteen. More general, for every even D, 5D+2 cases exist, whereas for every odd D, 5D+3 cases exist. For every D, exactly one half of them has the Euclidean signature. Our definition is well suited for the discussion of multidimensional cosmological models, and our results give a simple algorithm to decide whether a given metric represents the inflationary de Sitter spacetime (in unusual coordinates) or not.

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