Can Dark Matter be Geometry? A Case Study with Mimetic Dark Matter
  We investigate the possibility of dark matter being a pure geometrical
effect, rather than a particle or a compact object, by exploring a specific
modified gravity model: mimetic dark matter. We present an alternative
formulation of the theory, closer to the standard cosmological perturbation
theory framework. We make manifest the presence of arbitrary parameters and
extra functions, both at background level and at first order in perturbation
theory. We present the full set of independent equations of motion for this
model, and we discuss the amount of tuning needed to match predictions of the
theory to actual data. By using the matter power spectrum and cosmic microwave
background angular power spectra as benchmark observables, we explicitly show
that since there is no natural mechanism to generate adiabatic initial
conditions in this specific model, extra fine-tuning is required. We modify the
publicly available Boltzmann code \texttt{CLASS} to make accurate predictions
for the observables in mimetic dark matter. Our modified version of
\texttt{CLASS} is available on GitHub. We have used mimetic dark matter as an
illustration of how much one is allowed to change the initial conditions before
contradicting observations when modifying the laws of gravity as described by
General Relativity but we point out that modifying gravity without providing a
natural mechanism to generate adiabatic initial conditions will always lead to
highly fine-tuned models.
