Cosmology in the nonlinear domain

The introduction of a so-called dark sector in cosmology resolved
many inconsistencies between cosmological theory and observation,
but it also triggered many new questions. Dark Matter (DM)
explained gravitational effects beyond what is accounted for by
observed luminous matter and Dark Energy (DE) accounted for the
observed accelerated expansion of the universe. The most sought
after discoveries in the field would give insight into the nature
of these dark components. Dark Matter is considered to be the
better established of the two, but the understanding of its nature
may still lay far in the future. This thesis is concerned with
explaining and eliminating the discrepancies between the current
theoretical model, the standard model of cosmology, containing the
cosmological constant Λ as the driver of accelerated expansion and
Cold Dark Matter (CDM) as main source of gravitational effects, and
available observational evidence pertaining to the dark sector. In
particular, we focus on the small, galaxy-sized scales and below,
where N-body simulations of cosmological structure in the ΛCDM
universe predict much more structure and therefore much more power
in the matter power spectrum than what is found by a range of
different observations. This discrepancy in small scale power
manifests itself for example through the well known "dwarf-galaxy
problem'" (e.g. Klypin, 1999), the density profiles and
concentrations of individual haloes (Donato, 2009) as well as the
properties of voids (Tikhonov, 2009). A physical process that would
suppress the fluctuations in the dark matter density field might be
able to account for these discrepancies. Free-streaming dark matter
particles dampen the overdensities on small scales of the initial
linear matter density field. This corresponds to a suppression of
power in the linear matter power spectrum and can be modeled
relatively straightforwardly for an early decoupled thermal relic
dark matter particle. Such a particle would be neutrino-like, but
heavier; an example being the gravitino in the scenario, where it
is the Lightest Supersymmetric Particle and it decouples much
before neutrinos, but while still relativistic. Such a particle is
not classified as Hot Dark Matter, like neutrinos, because it only
affects small scales as opposed to causing a suppression at all
scales. However, its free-streaming prevents the smallest
structures from gravitationally collapsing and does therefore not
correspond to Cold Dark Matter. The effect of this Warm Dark Matter
(WDM) may be observable in the statistical properties of
cosmological Large Scale Structure. The suppression of the linear
matter density field at high redshifts in the WDM scenario can be
calculated by solving the Boltzmann equations. A fit to the
resulting linear matter power spectrum, which describes the
statistical properties of this density field in the simple thermal
relic scenario is provided by Viel (2004). This linear matter power
spectrum must then be corrected for late-time non-linear collapse.
This is rather difficult already in the standard cosmological
scenario, because exact solutions the the evolution of the
perturbed density field in the nonlinear regime cannot be found.
The widely used approaches are to the 'halofit' method of Smith
(2002), which is essentially a physically motivated fit to the
results of numerical simulations or using the even more physical,
but slightly less accurate halo model. However, both of these
non-linear methods were developed assuming only CDM and are
therefore not necessarily appropriate for the WDM case. In this
thesis, we modify the halo model (see also Smith, 2011) in order to
better accommodate the effects of the smoothed WDM density field.
Firstly, we treat the dark matter density field as made up of two
components: a smooth, linear component and a non-linear component,
both with power at all scales. Secondly, we introduce a cut-off
mass scale, below which no haloes are found. Thirdly, we suppress
the mass function also above the cut-off scale and finally, we
suppress the centres of halo density profiles by convolving them
with a Gaussian function, whose width depends on the WDM relic
thermal velocity. The latter effect is shown to not be significant
in the WDM scenario for the calculation of the non-linear matter
power spectrum at the scales relevant to the present and near
future capabilities of astronomical surveys in particular the
Euclid weak lensing survey. In order to determine the validity of
the different non-linear WDM models, we run cosmological
simulations with WDM (see also Viel, 2012) using the cutting edge
Lagrangian code Gadget-2 (Springel, 2005). We provide a fitting
function that can be easily applied to approximate the non-linear
WDM power spectrum at redshifts z = 0.5 - 3.0 at a range of scales
relevant to the weak lensing power spectrum. We examine the simple
thermal relic scenario for different WDM masses and check our
results against resolution issues by varying the size and number of
simulation particles. We finally briefly discuss the possibility
that the effects of WDM on the matter power spectrum might resemble
the analogous, but weaker and larger scale effects of the
free-streaming of massive neutrinos. We consider this with the goal
of re-examining the Sloan Digital Sky Survey data (as in Thomas,
2010). We find that the effects of the neutrinos might just differ
enough from the effects of WDM to prevent the degeneracy of the
relevant parameters, namely the sum of neutrino masses and the mass
of the WDM particle.