Practical approach to cosmological perturbations in modified gravity

Abstract

The next generation of large scale surveys will not only measure cosmological parameters within the framework of general relativity, but will also allow for precision tests of the framework itself. At the order of linear perturbations, departures from the growth in the standard cosmological model can be quantified in terms of two functions of time and Fourier number $k$. We argue that in local theories of gravity, in the quasistatic approximation, these functions must be ratios of polynomials in $k$, with the numerator of one function being equal to the denominator of the other. Moreover, the polynomials are even and of second degree in practically all viable models considered today. This means that, without significant loss of generality, one can use data to constrain only five functions of a single variable, instead of two functions of two variables. Furthermore, since the five functions are expected to be slowly varying, one can fit them to data in a nonparametric way with the aid of an explicit smoothness prior. We discuss practical application of this parametrization to forecasts and fits.