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

## TL;DR

This paper explores whether dark matter could be explained purely as a geometric effect within a modified gravity framework called mimetic dark matter, analyzing its theoretical consistency and observational viability.

## Contribution

It provides a reformulation of mimetic dark matter theory, assesses its initial condition tuning, and modifies a Boltzmann code to predict cosmological observables.

## Key findings

- No natural mechanism for adiabatic initial conditions in the model.
- Significant fine-tuning is required to match observational data.
- Modified code enables accurate predictions for cosmological observables.

## Abstract

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.