Effective Theory of Interacting Dark Energy

TL;DR

This work develops an effective theory of interacting dark energy that generalizes Horndeski-like gravity to allow non-universal conformal and disformal couplings between multiple matter species and the gravitational sector. The authors formulate the theory in the ADM/unity gauge, derive background and linear perturbation equations, and identify stability conditions that guarantee absence of ghosts and gradient instabilities, including the impact of disformal couplings on the kinetic sector. The framework introduces four gravity-sector parameters, α_K, α_B, α_M, α_T, plus two coupling parameters per species, α_C,I and α_D,I, with frame-redundancy reducing the independent set to 2(N_S+1). They illustrate two concrete scenarios—nonminimal CDM coupling and coupling to a relativistic fluid—showing how modified gravity and matter couplings jointly alter growth, potentials, and lensing observables, and providing a path to constrain these deviations with data. The formalism thus offers a comprehensive, gauge-invariant toolkit for interpreting cosmological probes of dark energy and gravity beyond ΛCDM.

Abstract

We present a unifying treatment of dark energy and modified gravity that allows distinct conformal-disformal couplings of matter species to the gravitational sector. In this very general approach, we derive the conditions to avoid ghost and gradient instabilities. We compute the equations of motion for background quantities and linear perturbations. We illustrate our formalism with two simple scenarios, where either cold dark matter or a relativistic fluid is nonminimally coupled. This extends previous studies of coupled dark energy to a much broader spectrum of gravitational theories.