Velocity-dependent interacting dark energy and dark matter with a Lagrangian description of perfect fluids

Understand

We consider a cosmological scenario where the dark sector is described by two perfect fluids that interact through a velocity-dependent coupling.

• This coupling gives rise to an interaction in the dark sector driven by the relative velocity of the components, thus making the background evolution oblivious to the interaction and only the perturbed Euler equations are affected at first order.
• We obtain the equations governing this system with the Schutz-Sorkin Lagrangian formulation for perfect fluids and derive the corresponding stability conditions to avoid ghosts and Laplacian instabilities.
• As a particular example, we study a model where dark energy behaves as a radiation fluid at high redshift while it effectively becomes a cosmological constant in the late Universe.