Classification of multidimensional inflationary models

TL;DR

This paper classifies constant curvature spacetimes in various signatures and dimensions, providing an algorithm to identify inflationary de Sitter models within multidimensional cosmology.

Contribution

It introduces a classification scheme for multi-warped product spacetimes and offers a practical algorithm to recognize inflationary de Sitter metrics.

Findings

Classified constant curvature spaces for various dimensions and signatures.

Identified specific counts of representations for D=2 and D=3.

Developed an algorithm to distinguish inflationary de Sitter spacetimes.

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.