  It has been claimed that the standard model of cosmology (LCDM) cannot easily
account for a number of observations on relatively small scales, motivating
extensions to the standard model. Here we introduce a new suite of cosmological
simulations that systematically explores three plausible extensions: warm dark
matter, self-interacting dark matter, and a running of the scalar spectral
index of density fluctuations. Current observational constraints are used to
specify the additional parameters that come with these extensions. We examine a
large range of observable metrics on small scales, including the halo mass
function, density and circular velocity profiles, the abundance of satellite
subhaloes, and halo concentrations. For any given metric, significant
degeneracies can be present between the extensions. In detail, however, the
different extensions have quantitatively distinct mass and radial dependencies,
suggesting that a multi-probe approach over a range of scales can be used to
break the degeneracies. We also demonstrate that the relative effects on the
radial density profiles in the different extensions (compared to the standard
model) are converged down to significantly smaller radii than are the absolute
profiles. We compare the derived cosmological trends with the impact of
baryonic physics using the EAGLE and ARTEMIS simulations. Significant
degeneracies are also present between baryonic physics and cosmological
variations (with both having similar magnitude effects on some observables).
Given the inherent uncertainties both in the modelling of galaxy formation
physics and extensions to LCDM, a systematic and simultaneous exploration of
both is strongly warranted.
