Scale Factor Self-Dual Cosmological Models

TL;DR

This paper introduces a conformal time scale factor duality in cosmological models, linking different universe phases and fluids, with applications to inflation and dark energy, revealing new scalar field interactions and dualities.

Contribution

It develops a self-dual cosmological framework using conformal time scale factor duality, connecting scalar field models with modified Chaplygin gas and Kähler sigma models.

Findings

Identifies a UV/IR duality in cosmological models.

Links self-duality to specific equations of state for fluids.

Proposes scalar field interactions compatible with duality.

Abstract

We implement a conformal time scale factor duality for Friedmann-Robertson-Walker cosmological models, which is consistent with the weak energy condition. The requirement for self-duality determines the equations of state for a broad class of barotropic fluids. We study the example of a universe filled with two interacting fluids, presenting an accelerated and a decelerated period, with manifest UV/IR duality. The associated self-dual scalar field interaction turns out to coincide with the "radiation-like" modified Chaplygin gas models. We present an equivalent realization of them as gauged K\"ahler sigma models (minimally coupled to gravity) with very specific and interrelated K\"ahler- and super-potentials. Their applications in the description of hilltop inflation and also as quintessence models for the late universe are discussed.