Dark Energy, Inflation and Extra Dimensions

TL;DR

This paper explores how accelerated cosmic expansion, like inflation and dark energy, constrains higher-dimensional theories, especially under the null energy condition, affecting their viability and properties.

Contribution

It provides new constraints on higher-dimensional theories with compactification, showing how accelerated expansion phases impose strict conditions on these models.

Findings

Inflation is impossible for many compactifications if the null energy condition holds.

Dark energy consistent with observations requires time-varying Newton's constant and dark energy equation-of-state.

Violations of the null energy condition allow for inhomogeneous and synchronized compactification dynamics.

Abstract

We consider how accelerated expansion, whether due to inflation or dark energy, imposes strong constraints on fundamental theories obtained by compactification from higher dimensions. For theories that obey the null energy condition (NEC), we find that inflationary cosmology is impossible for a wide range of compactifications; and a dark energy phase consistent with observations is only possible if both Newton's gravitational constant and the dark energy equation-of-state vary with time. If the theory violates the NEC, inflation and dark energy are only possible if the NEC-violating elements are inhomogeneously distributed in thecompact dimensions and vary with time in precise synchrony with the matter and energy density in the non-compact dimensions. Although our proofs are derived assuming general relativity applies in both four and higher dimensions and certain forms of metrics, we argue that similar constraints must apply for more general compactifications.