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We investigate the possibility of dark matter being a pure geometricaleffect, rather than a particle or a compact object, by exploring a specificmodified gravity model: mimetic dark matter. We present an alternativeformulation of the theory, closer to the standard cosmological perturbationtheory framework. We make manifest the presence of arbitrary parameters andextra functions, both at background level and at first order in perturbationtheory. We present the full set of independent equations of motion for thismodel, and we discuss the amount of tuning needed to match predictions of thetheory to actual data. By using the matter power spectrum and cosmic microwavebackground angular power spectra as benchmark observables, we explicitly showthat since there is no natural mechanism to generate adiabatic initialconditions in this specific model, extra fine-tuning is required. We modify thepublicly available Boltzmann code \texttt{CLASS} to make accurate predictionsfor the observables in mimetic dark matter. Our modified version of\texttt{CLASS} is available on GitHub. We have used mimetic dark matter as anillustration of how much one is allowed to change the initial conditions beforecontradicting observations when modifying the laws of gravity as described byGeneral Relativity but we point out that modifying gravity without providing anatural mechanism to generate adiabatic initial conditions will always lead tohighly fine-tuned models.

Can Dark Matter be Geometry? A Case Study with Mimetic Dark Matter