Unified Dark Energy and Dust Dark Matter Dual to Quadratic Purely Kinetic K-Essence

TL;DR

This paper presents a duality between a modified gravity plus scalar field model unifying dark energy and dark matter, and a quadratic purely kinetic k-essence model, including analysis of its quantum cosmology.

Contribution

It introduces a duality linking a modified gravity-scalar field model with unified dark energy and dark matter to a quadratic kinetic k-essence model, extending previous work.

Findings

Explicit duality between the models established.

Effective action derived in Einstein frame.

Quantum cosmology aspects briefly discussed.

Abstract

We consider a modified gravity plus single-scalar-field model, where the scalar Lagrangian couples symmetrically both to the standard Riemannian volume-form (spacetime integration measure density) given by the square-root of the determinant of the Riemannian metric, as well as to another non-Riemannian volume-form in terms of an auxiliary maximal-rank antisymmetric tensor gauge field. As shown in a previous paper, the pertinent scalar field dynamics provides an exact unified description of both dark energy via dynamical generation of a cosmological constant, and dark matter as a "dust" fluid with geodesic flow as a result of a hidden Noether symmetry. Here we extend the discussion by considering a non-trivial modification of the purely gravitational action in the form of f(R) = R - \alpha R^2 generalized gravity. Upon deriving the corresponding "Einstein-frame" effective action of the latter modified gravity-scalar-field theory we find explicit duality (in the sense of weak versus strong coupling) between the original model of unified dynamical dark energy and dust fluid dark matter, on one hand, and a specific quadratic purely kinetic "k-essence" gravity-matter model with special dependence of its coupling constants on only two independent parameters, on the other hand. The canonical Hamiltonian treatment and Wheeler-DeWitt quantization of the dual purely kinetic "k-essence" gravity-matter model is also briefly discussed.