Designing Horndeski and the effective fluid approach

Abstract

We present a family of designer Horndeski models, i.e., models that have a background exactly equal to that of the ΛCDM model but perturbations given by the Horndeski theory. Then, we extend the effective fluid approach to Horndeski theories, providing simple analytic formulas for the equivalent dark energy effective fluid pressure, density, and velocity. We implement the dark energy effective fluid formulas in our code efclass, a modified version of the widely used Boltzmann solver class, and compare the solution of the perturbation equations with those of the code hi-class which already includes Horndeski models. We find that our simple modifications to the vanilla code are accurate to the level of ∼0.1% with respect to the more complicated hi-class code. Furthermore, we study the kinetic braiding model both on and off the attractor, and we find that even though the full case has a proper ΛCDM limit for large n, it is not appropriately smooth, thus causing the quasistatic approximation to break down. Finally, we focus on our designer model (HDES), which has both a smooth ΛCDM limit and well-behaved perturbations, and we use it to perform Markov Chain-Monte Carlo analyses to constrain its parameters with the latest cosmological data. We find that our HDES model can also alleviate the soft 2σ tension between the growth data and Planck 18 due to a degeneracy between σ8 and one of its model parameters that indicates the deviation from the ΛCDM model.