Do cosmological data rule out $f(\mathcal{R})$ with $w\neq-1$?

Understand

We review the Equation of State (EoS) approach to dark sector perturbations and apply it to $f(\mathcal{R})$ gravity models of dark energy.

• We show that the EoS approach is numerically stable and use it to set observational constraints on designer models.
• Within the EoS approach we build an analytical understanding of the dynamics of cosmological perturbations for the designer class of $f(\mathcal{R})$ gravity models, characterised by the parameter $B_0$ and the background equation of state of dark energy $w$.
• When we use the Planck Cosmic Microwave Background (CMB) temperature anisotropy, polarisation and lensing data as well as the Baryonic Acoustic Oscillation (BAO) data from SDSS and WiggleZ, we find $B_0<0.006$ (95\%CL) for the designer models with $w=-1$.