Parametrising non-linear dark energy perturbations

In this paper, we quantify non-linear effects from k-essence dark energy through an effective parameter μ that encodes the additional contribution of a dark energy fluid or a modification of gravity to the Poisson equation. This is a first step toward quantifying the non-linear effects of dark energy/modified gravity models in a more general approach. We compare our simulation results with predictions from the linear Boltzmann code 𝙲𝙻𝙰𝚂𝚂. We show that for a large k-essence speed of sound the 𝙲𝙻𝙰𝚂𝚂 results are sufficiently accurate, while for a low speed of sound non-linearities in matter and in the k-essence field are non-negligible. We propose a tanh-based parameterisation for μ to include the non-linear effects based on the simulation results and this parametric form of μ can be used to improve Fisher forecasts or Newtonian N-body simulations for k-essence models.