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

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 $w_{\mathrm{eff}}\ne 0$ 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.

23 pages + references; accepted for publication in PRD

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• A clarification on prevailing misconceptions in unimodular gravity
• Planckian discreteness as seeds for cosmic structure
• Cosmological constant as an integration constant
• Reconstruction of inflationary scenarios in non-conservative unimodular gravity
• Climbing over the potential barrier during inflation via null energy condition violation
• Stochastic dark matter: Covariant Brownian motion from Planckian discreteness
• Higgs Inflation in Unimodular Gravity
• Charged thin shells in unimodular gravity
• Probing Interacting Dark Sectors with upcoming Post-Reionization and Galaxy Surveys