Kinetic field theory: effects of modified gravity theories with screening mechanisms on non-linear cosmic density fluctuations

Abstract: In a mean-field approximation within Kinetic Field Theory, it is possible to derive an accurate analytic expression for the power spectrum of present-day non-linear cosmic density fluctuations. It depends on the theory of gravity and the cosmological model via the expansion function of the background space-time, the growth factor derived from it, and the gravitational coupling strength, which may deviate from Newton's constant in a manner depending on time and spatial scale. In earlier work [1], we introduced a functional Taylor expansion around general relativity and the cosmological standard model to derive the effects of a wide class of modified-gravity theories on the non-linear power spectrum, assuming that such effects need to be small given the general success of the standard model. Here, we extend this class towards theories with small-scale screening, modeling screening effects by a suitably flexible interpolating function. We compare the Taylor expansion with full mean-field solutions and find good agreement where expected. We find typical relative enhancements of the non-linear power spectrum between a few and a few ten per cent in a broad range of wave numbers between $k\gtrsim0.1-10\,h\,\mathrm{Mpc}^{-1}$, in good qualitative agreement with results of numerical simulations. Taking nDGP gravity as a quantitative example we compare our results to N-body simulations and find percent-level agreement for wavenumbers $k\lesssim 2\,h\,\text{Mpc}^{-1}$, if the scale where screening sets in, $k^*$, is adapted appropriately. This extends the application of our analytic approach to non-linear cosmic structure formation to essentially all classes of modified-gravity theories.