U-duality Covariant M-theory Cosmology

TL;DR

The paper develops a manifestly U-duality covariant cosmological framework by reducing 11D supergravity on a Ricci-flat internal space to a D-dimensional external theory with a single breathing modulus, yielding an $SL(n)/SO(n)$ sigma-model structure for the internal sector. It treats the external U-duality groups $G = SL(2)×SL(3)$ for D=4 and $G = SL(5)$ for D=5, and derives a one-dimensional effective action that can be solved covariantly. The authors show that asymptotic cosmological expansion powers and Hubble parameters are invariant under the external U-duality, while duality transformations shift the transition time between asymptotic KK regions and control the transition details; in D=5, duality combined with time reversal can map expanding negative- and positive-time branches into each other. They illustrate explicit FRW solutions in both D=4 and D=5, discuss the implications for pre-big-bang–type scenarios, and highlight how dualities organize the space of cosmological solutions in M-theory, albeit with caveats regarding horizon-based interpretations due to nonlocality in time.

Abstract

A manifestly U-duality covariant approach to M-theory cosmology is developed and applied to cosmologies in dimensions D=4,5. Cosmological properties such as expansion powers and Hubble parameters turn out to be U-duality invariant in certain asymptotic regions. U-duality transformations acting on cosmological solutions, on the other hand, shift the transition time between two asymptotic regions and determine the details of the transition. Moreover, in D=5, we show that U-duality can map expanding negative and positive branch solutions into each other.