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.