The Parameterized Post-Friedmannian Framework for Interacting Dark Energy Theories

TL;DR

The work addresses the challenge of testing a broad landscape of interacting dark energy models by extending the Parameterized Post-Friedmannian (PPF) framework to include a scalar field coupled to dark matter. It develops a gauge-invariant, two-component (GDM and DE) perturbative formalism in which dark-sector energy–momentum exchange is encoded by a background current $J_ u$ with a background function $Q( au)$ and perturbations $q$ and $S$, and then reduces the problem to a finite set of coefficient functions that map to known models. Through worked examples (coupled quintessence, $J_ u abla_ u u_ u$-type models, elastic scattering) and the three model types from Pourtsidou:2013aa (Type-1, Type-2, Type-3), the authors provide explicit mappings of the Lagrangian/dynamics to the PPF coefficients, demonstrating significant parameter-space reduction while preserving model-independence for data testing. The framework enables efficient phenomenological classification, facilitates reconstruction of underlying Lagrangians from PPF coefficients, and points toward numerical implementations to constrain dark-sector couplings with current and future data.

Abstract

We present the most general parametrisation of models of dark energy in the form of a scalar field which is explicitly coupled to dark matter. We follow and extend the Parameterized Post-Friedmannian approach, previously applied to modified gravity theories, in order to include interacting dark energy. We demonstrate its use through a number of worked examples and show how the initially large parameter space of free functions can be significantly reduced and constrained to include only a few non-zero coefficients. This paves the way for a model-independent approach to classify and test interacting dark energy theories.