Designing Horndeski and the effective fluid approach

Understand

We present a family of designer Horndeski models, i.e.

• models that have a background exactly equal to that of the $\Lambda$CDM model but perturbations given by the Horndeski theory.
• Then, we extend the effective fluid approach to Horndeski theories, providing simple analytic formulae for the equivalent dark energy effective fluid pressure, density and velocity.
• We implement the dark energy effective fluid formulae 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.