Duality linking standard and tachyon scalar field cosmologies

TL;DR

This paper explores the duality between standard and tachyon scalar field cosmologies, showing it generally breaks at the perturbative level but remains at linear order for slow-rolling fields, with explicit examples provided.

Contribution

It derives the transformation linking standard and tachyon scalar fields and potentials, and analyzes the conditions under which duality holds or breaks.

Findings

Duality is broken at the perturbative level for general cases.

Duality is preserved at linear order for slow-rolling fields.

Explicit examples demonstrate the scalar-tachyon correspondence.

Abstract

In this work we investigate the duality linking standard and tachyon scalar field cosmologies. We determine the transformation between standard and tachyon scalar fields and between their associated potentials, corresponding to the same background evolution. We show that, in general, the duality is broken at a perturbative level, when deviations from a homogeneous and isotropic background are taken into account. However, we find that for slow-rolling fields the duality is still preserved at a linear level. We illustrate our results with specific examples of cosmological relevance, where the correspondence between scalar and tachyon scalar field models can be calculated explicitly.