  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.
