Large scale structure of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>f</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>R</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math>gravity

We study the evolution of linear cosmological perturbations in $f(R)$ models of accelerated expansion in the physical frame where the gravitational dynamics are fourth order and the matter is minimally coupled. These models predict a rich and testable set of linear phenomena. For each expansion history, fixed empirically by cosmological distance measures, there exists two branches of $f(R)$ solutions that are parametrized by $B\ensuremath{\propto}{d}^{2}f/d{R}^{2}$. For $B&lt;0$, which include most of the models previously considered, there is a short-timescale instability at high curvature that spoils agreement with high redshift cosmological observables. For the stable $B&gt;0$ branch, $f(R)$ models can reduce the large-angle CMB anisotropy, alter the shape of the linear matter power spectrum, and qualitatively change the correlations between the CMB and galaxy surveys. All of these phenomena are accessible with current and future data and provide stringent tests of general relativity on cosmological scales.