Triality between Inflation, Cyclic and Phantom Cosmologies

TL;DR

This paper explores a novel duality and triality connecting different cosmological models, including inflationary, cyclic, and phantom universes, revealing deep relationships through scale factor and Hubble parameter transformations.

Contribution

It introduces a new duality framework linking accelerating, decelerating, and phantom cosmologies, extending to curved universes and braneworld scenarios.

Findings

Establishes a duality between accelerating and decelerating universes.

Identifies a triality involving inflation, cyclic, and phantom models.

Extends duality concepts to curved and braneworld cosmologies.

Abstract

It is shown that any spatially flat and isotropic universe undergoing accelerated expansion driven by a self-interacting scalar field can be directly related to a contracting, decelerating cosmology. The duality is made manifest by expressing the scale factor and Hubble parameter as functions of the scalar field and simultaneously interchanging these two quantities. The decelerating universe can be twinned with a cosmology sourced by a phantom scalar field by inverting the scale factor and leaving the Hubble parameter invariant. The accelerating model can be related to the same phantom universe by identifying the scale factor with the inverse of the Hubble parameter. The duality between accelerating and decelerating backgrounds can be extended to spatially curved cosmologies and models containing perfect fluids. A similar triality and associated scale factor duality is found in the Randall-Sundrum type II braneworld scenario.