Interacting dark sector from the trace-free Einstein equations: cosmological perturbations with no instability

TL;DR

This paper develops a framework for interacting dark energy models within trace-free Einstein gravity, deriving perturbation equations and demonstrating the absence of large-scale instabilities in specific models.

Contribution

It introduces a new approach to modeling interacting dark energy using trace-free Einstein equations and analyzes perturbations showing stability in certain scenarios.

Findings

Large-scale instability is absent in the proposed model.

Energy transfer from dark matter to dark energy avoids gradient instability.

Interacting dark energy with w=-1 is equivalent to generalized dark matter.

Abstract

In trace-free Einstein gravity, the stress-energy tensor of matter is not necessarily conserved and so the theory offers a natural framework for interacting dark energy models where dark energy has a constant equation of state $w=-1$. We derive the equations of motion for linear cosmological perturbations in interacting dark energy models of this class, focusing on the scalar sector. Then, we consider a specific model where the energy-momentum transfer potential is proportional to the energy density of cold dark matter; this transfer potential has the effect of inducing an effective equation of state $w_{\rm eff}\neq0$ for cold dark matter. We analyze in detail the evolution of perturbations during radiation domination on super-Hubble scales, finding that the well-known large-scale instability that affects a large class of interacting dark energy models is absent in this model. To avoid a gradient instability, energy must flow from dark matter to dark energy. Finally, we show that interacting dark energy models with $w=-1$ are equivalent to a class of generalized dark matter models.