Unraveling the effective fluid approach for $f(R)$ models in the subhorizon approximation

Understand

We provide explicit formulas for the effective fluid approach of $f(R)$ theories, such as the Hu & Sawicki and the designer models.

• Using the latter and simple modifications to the CLASS code, which we call EFCLASS, in conjunction with very accurate analytic approximations for the background evolution, we obtain competitive results in a much simpler and less error-prone approach.
• We also derive the initial conditions in matter domination and we find they differ from those already found in the literature for a constant $w$ model.
• A clear example is the designer model that behaves as $\Lambda$CDM in the background, but has nonetheless dark energy perturbations.