# Kinetic Field Theory applied to Vector-Tensor Gravity

## TL;DR

This paper applies kinetic field theory to analyze non-linear cosmic structure formation within vector-tensor gravity theories, offering an analytical approach that complements and potentially surpasses traditional numerical simulations.

## Contribution

It introduces the first application of kinetic field theory to vector-tensor gravity, providing a new analytical method for studying non-linear cosmic structures in these theories.

## Key findings

- Analytic non-linear power spectrum matches simulations up to certain scales.
- First study applying kinetic field theory to vector-tensor gravity.
- Demonstrates potential of analytical methods in alternative gravity models.

## Abstract

The formation of cosmic structures is an important diagnostic for both the dynamics of the cosmological model and the underlying theory of gravity. At the linear level of these structures, certain degeneracies remain between different cosmological models and alternative gravity theories. It is thus indispensable to study the non-linear, late-time evolution of cosmic structures to try and disentangle their fundamental properties caused by the cosmological model or gravity theory itself. Conventionally, non-linear cosmic structure formation is studied by means of computationally expensive numerical simulations. Since these inevitably suffer from shot noise and are too time consuming to systematically scrutinize large parameter spaces of cosmological models or fundamental theories, analytical methods are needed to overcome the limitations of numerical simulations. Recently, a new analytic approach to non-linear cosmic structure formation has been proposed based on kinetic field theory for classical particle ensembles. Within this theory, a closed, analytic, non-perturbative and parameter-free equation could be derived for the non-linear power spectrum of cosmic density perturbations which agrees very well with numerically simulated results to wave numbers $k\lesssim10\,h\,\mathrm{Mpc}^{-1}$ at redshift $z = 0$. In this Letter, we study for the first time the implications of alternative gravity theories for non-linear cosmic structure formation applying this promising new analytic framework. As an illustrative example, we consider vector-tensor theories, which support very interesting isotropic cosmological solutions.