Scale Factor Duality and the Energy Condition Inequalities

TL;DR

This paper explores the duality between scale factor transformations in cosmology and the Weak Energy Condition, revealing a connection that could extend to more general spacetime transformations.

Contribution

It demonstrates a duality between scale factor duality and WEC violation in cosmological models, suggesting a possible generalization to O(d,d) related spacetimes.

Findings

Scale factor duality correlates with WEC violation in cosmology.

Specific O(d,d) transformations hint at a broader duality.

Implications for energy conditions in string-inspired cosmological models.

Abstract

We demonstrate, by a simple analysis, that cosmological line elements related by scale factor duality also exhibit a duality with respect to the conservation/violation of the Weak Energy Condition (WEC) by the matter that acts as the source in the one-loop beta function equations for the metric coupling written explicitly in the form of the Einstein equations. Furthermore, a study of specific pairs of line elements (obtained via O(d,d) transformations) hints at a possible generalisation of the above duality w.r.t. WEC for the case of O(d,d) related spacetimes. Consequences and extensions thereof are also pointed out.