A fast route to modified gravitational growth
The growth rate of the large-scale structure of the Universe has been advocated as the observable par excellence for testing gravity on cosmological scales. By considering linear-order deviations from general relativity, we show that corrections to the growth rate, $f$, can be expressed as an integral over a ``source'' term, weighted by a theory-independent ``response kernel.'' This leads to an efficient and accurate ``plug-and-play'' expression for generating growth rates in alternative gravity theories, bypassing lengthy theory-specific computations. We use this approach to explicitly show that $f$ is sensitive to a degenerate combination of modified expansion and modified clustering effects. Hence the growth rate, when used in isolation, is not a straightforward diagnostic of modified gravity.