Cosmological Evidence Modelling: a new simulation-based approach to
  constrain cosmology on non-linear scales
  Extracting accurate cosmological information from galaxy-galaxy and
galaxy-matter correlation functions on non-linear scales ($\lesssim 10 h^{-1}
\mathrm{Mpc}$) requires cosmological simulations. Additionally, one has to
marginalise over several nuisance parameters of the galaxy-halo connection.
However, the computational cost of such simulations prohibits naive
implementations of stochastic posterior sampling methods like Markov chain
Monte Carlo (MCMC) that would require of order $\mathcal{O}(10^6)$ samples in
cosmological parameter space. Several groups have proposed surrogate models as
a solution: a so-called emulator is trained to reproduce observables for a
limited number of realisations in parameter space. Afterwards, this emulator is
used as a surrogate model in an MCMC analysis. Here, we demonstrate a different
method called Cosmological Evidence Modelling (CEM). First, for each
simulation, we calculate the Bayesian evidence marginalised over the
galaxy-halo connection by repeatedly populating the simulation with galaxies.
We show that this Bayesian evidence is directly related to the posterior
probability of cosmological parameters. Finally, we build a physically
motivated model for how the evidence depends on cosmological parameters as
sampled by the simulations. We demonstrate the feasibility of CEM by using
simulations from the Aemulus simulation suite and forecasting cosmological
constraints from BOSS CMASS measurements of redshift-space distortions. Our
analysis includes an exploration of how galaxy assembly bias affects
cosmological inference. Overall, CEM has several potential advantages over the
more common approach of emulating summary statistics, including the ability to
easily marginalise over highly complex models of the galaxy-halo connection and
greater accuracy, thereby reducing the number of simulations required.
