A Note on 4d Kination and Higher-Dimensional Uplifts

TL;DR

This work investigates the link between 4d kination epochs in string cosmology and 10d Kasner spacetimes, extending the prior IIB-focused analysis to IIA, heterotic, Type I, and M-theory. It builds a two-moduli 4d EFT with a kination solution, derives explicit 10d uplifts (Mueller-type Kasner metrics) and a consistency condition $m \alpha^2 + n \beta^2 = \dfrac{4}{3}$, and shows how the 4d dynamics are mirrored in 10d via the relation $g_{4d,E}=e^{-2\phi}\mathcal{V} g_{4d,s}$. The paper also analyzes perturbations of the 10d Kasner background, mapping complex-structure, volume, and radiation modes to 4d fields on the kination background, and derives a detailed 4d effective action that reproduces the perturbative structure; it further studies winding-mode domination, finding a nontrivial expansion with $\rho \propto a^{-10/3}$ and $a(t) \propto t^{6/7}$. Overall, the results provide a concrete bridge from high-dimensional Kasner dynamics to observable post-inflation cosmology in string theory and offer a framework for testable predictions of early-universe kination epochs.

Abstract

This note expands on the details of the relationship between 4d kination solutions in string cosmology and Kasner solutions of 10d general relativity. It extends previous analyses of this relationship in IIB string theory to other string theories and also to 11d M-theory, while also providing extensive detail on the relationship between perturbations of the 10d Kasner metric and the presence of radiation and matter backgrounds in the dimensionally reduced 4d kination theory.