N-body simulations of structure formation in thermal inflation
  cosmologies
  Thermal inflation models (which feature two inflationary stages) can display
damped primordial curvature power spectra on small scales which generate damped
matter fluctuations. For a reasonable choice of parameters, thermal inflation
models naturally predict a suppression of the matter power spectrum on galactic
and sub-galactic scales, mimicking the effect of warm or interacting dark
matter. Matter power spectra in these models are also characterised by an
excess of power (w.r.t. the standard $\Lambda$CDM power spectrum) just below
the suppression scale. By running a suite of N-body simulations we investigate
the non-linear growth of structure in models of thermal inflation. We measure
the non-linear matter power spectrum and extract halo statistics, such as the
halo mass function, and compare these quantities with those predicted in the
standard $\Lambda$CDM model and in other models with damped matter
fluctuations. We find that the thermal inflation models considered here produce
measurable differences in the matter power spectrum from $\Lambda$CDM at
redshifts $z>5$, while the halo mass functions are appreciably different at all
redshifts. The halo mass function at $z=0$ for thermal inflation displays an
enhancement of around $\sim 20\%$ w.r.t. $\Lambda$CDM and a damping at lower
halo masses, with the position of the enhancement depending on the value of the
free parameter in the model. The enhancement in the halo mass function (w.r.t.
$\Lambda$CDM ) increases with redshift, reaching $\sim 40\%$ at $z=5$. We also
study the accuracy of the analytical Press-Schechter approach, using different
filters to smooth the density field, to predict halo statistics for thermal
inflation. We find that the predictions with the smooth-$k$ filter agree with
the simulation results over a wider range of halo masses than is the case with
other filters commonly used in the literature.
