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 CLASS to make accurate predictions for the observables in mimetic dark matter. Our modified version of CLASS is available on GitHub¹ . 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. Moreover, we point out that modifying gravity without providing a natural mechanism to generate adiabatic initial conditions will always lead to highly fine-tuned models.

通过探索特定的改良重力模型：模拟暗物质，我们研究了暗物质是纯几何效应而不是粒子或紧凑物体的可能性。我们提出了该理论的另一种表述，更接近标准的宇宙学扰动理论框架。我们在扰动理论中以背景水平和一阶来证明任意参数和额外函数的存在。我们提供了该模型的完整独立运动方程组，并讨论了使理论预测与实际数据匹配所需的调整量。通过使用物质功率谱和宇宙微波背景角功率谱作为基准可观测物，我们明确表明，由于在此特定模型中没有自然机制来产生绝热初始条件，因此需要额外的微调。我们修改了公开的玻尔兹曼代码对模拟暗物质中的可观察物做出准确预测的CLASS。我们的CLASS的修改版本可在GitHub ^1上获得。我们已使用模拟暗物质来说明按照相对论描述的修改引力定律时，在与观测值矛盾之前允许多少人改变初始条件。此外，我们指出，在没有提供自然机制来产生绝热初始条件的情况下修改引力总是会导致模型的精细调整。