Kinetic field theory: generic effects of alternative gravity theories on non-linear cosmic density-fluctuations

TL;DR

This paper develops a framework using kinetic field theory to analyze how alternative gravity theories can influence non-linear cosmic density fluctuations, enabling predictions for a broad class of modified gravity models.

Contribution

It introduces a first-order Taylor expansion of the non-linear power spectrum in KFT, linking it to background expansion and gravitational coupling in generalized gravity theories.

Findings

Framework applicable to various modified gravity models

Demonstration with generalized Proca theories

Potential to distinguish gravity theories via cosmic structure analysis

Abstract

Non-linear cosmic structures contain valuable information on the expansion history of the background space-time, the nature of dark matter, and the gravitational interaction. The recently developed kinetic field theory of cosmic structure formation (KFT) allows to accurately calculate the non-linear power spectrum of cosmic density fluctuations up to wave numbers of $k\lesssim10\,h\,\mathrm{Mpc}^{-1}$ at redshift zero. Cosmology and gravity enter this calculation via two functions, viz. the background expansion function and possibly a time-dependent modification of the gravitational coupling strength. The success of the cosmological standard model based on general relativity suggests that cosmological models in generalized theories of gravity should have observable effects differing only weakly from those in standard cosmology. Based on this assumption, we derive the functional, first-order Taylor expansion of the non-linear power spectrum of cosmic density fluctuations obtained from the mean-field approximation in KFT in terms of the expansion function and the gravitational coupling strength. This allows us to study non-linear power spectra expected in large classes of generalized gravity theories. To give one example, we apply our formalism to generalized Proca theories.