Constraining models of $f(R)$ gravity with Planck and WiggleZ power spectrum data

In order to explain cosmic acceleration without invoking "dark" physics, we consider $f(R)$ modified gravity models, which replace the standard Einstein-Hilbert action in General Relativity with a higher derivative theory. We use data from the WiggleZ Dark Energy survey to probe the formation of structure on large scales which can place tight constraints on these models. We combine the large-scale structure data with measurements of the cosmic microwave background from the Planck surveyor. After parameterising the modification of the action using the Compton wavelength parameter $B_0$, we constrain this parameter using ISiTGR, assuming an initial non-informative log prior probability distribution of this cross-over scale. We find that the addition of the WiggleZ power spectrum provides the tightest constraints to date on $B_0$ by an order of magnitude, giving ${\rm log}_{10}(B_0) < -4.07$ at 95% confidence limit. Finally, we test whether the effect of adding the lensing amplitude $A_{\rm Lens}$ and the sum of the neutrino mass $\sum m_\nu$ is able to reconcile current tensions present in these parameters, but find $f(R)$ gravity an inadequate explanation.