We don’t have a direct method of observing, it comes from very complicated analysis.

Alternative questions: What would be the motivation for studying modified gravity? Because dark matter and dark energy work very well as the simplest model.

There is a place for dark matter in the standard model, but its somewhat phenomenological and we put it in to match observations.
Are we in an analogous to Newtonian gravity -> GR 200 years ago? Dark matter is working well, but we don’t really know what it is.
Is there a general consensus that QM is more fundamental, so it has to be GR that is modified and quantized, rather than giving up QM first?

The thing that we really know is that with the existing fully developed theories of physics cosmology doesn’t add up. If it were just dark matter we could attribute it to some undetected particle. But then we have to include interactions with other matter etc. But then what about dark energy. The fact that there are two things we have to put in by end hints that it is not fundamental.
In larger length scales could we have more corrections to GR.

Dark matter and dark energy can be both a misunderstood observational effect as well as a signature of modified gravity. There are several arguments that support both thesis.  Both of these thesis are based on the strong and compelling experimental evidence  provided by observations. In particular, evidence of the expansion of the universe and the measurements of the microwave radiation show that dark energy and dark matter is something that theoretical descriptions have to account for. If one believes that the huge amount of data has been processed and interpreted correctly, then dark energy and dark matter can be a signature of modified gravity. However, the present theories of modified gravity do not agree to perfection with the experimental data when simulations are done under the assumptions of these theories. This also poses the question of which theories of modified gravity are useful and fundamentally correct. This question can be also rephrased as: which fundamental physical properties are we willing to let go in order to obtain a theory that correctly incorporates a description of dark matter and dark energy? The fact that most of the current modified gravity do not incorporate a description of dark energy and dark gravity may imply that dark matter and dark energy may come from misinterpreting the experimental data. Since the amount of data is so big there is a huge tuning space in which there is room for different interpretations of it. In summary, this is still an open question in which both possibilities are equally likely.
Suppose we accept the modified gravity, does it eventually lead to a kind of dark matter particle after we quantize it? In principle we can. But usually the dark matter takes place in a perturbative theory and quantizing gravity yields non-perturbative theory. After quantize modified gravity, one may just get some additional modes of graviton.

We have enough evidence that the expansion of the universe is real, not a misunderstanding.

The number of experiments confirming dark matter is far more than dark energy.  Explaining dark matter with modified gravity is much harder, since there are  evidence for dark matter from different areas and different experiments. 

Dark energy detection comes from homogenous Friedmann equation while dark  matter has many more observational confirmation.

Bullet cluster – position of dark matter constrains whether it’s possible to have modified gravity instead of

Is modified gravity really different from dark matter because of quantization

Modified gravity as modified space-time
Evidence for dark energy: anisotropy, supernovae, saxe-wolf effect

Working on constraints to dark energy equation of state

There is an important distinction between dark matter and dark energy. The only evidence we have for dark energy is the observation that the expansion of the universe is accelerating. In contrast, for dark matter we have many different observations. Therefore we are much more confident that dark matter exists than we are about dark energy. It might be that a modified gravity theory could explain the accelerating universe, but it will have a much harder time to explain all the different observations currently explained by dark matter, on both small and large scales.

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