Classification of multidimensional inflationary models

Abstract

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.