Dark Matter vs Modified Gravity Why do cosmologists and astrophysicists assume that the reason for the higher velocities of outer stars in galaxies is due to matter at all? The name dark matter seems misleading. Couldn't gravity just work different on larger scales? After years of searching for a dark matter 'particle', we still have nothing. I'm a little puzzled at the constant search for a weakly interacting particle.
 A: Cosmologists and astrophysicists are not assuming anything. They are looking for evidence that will either identify the dark matter particle or show that it doesn't exist. Sometimes, this takes a long time. Nearly 50 years passed between the original 1964 papers predicting the Higgs boson and the discovery at CERN in 2013 (further study of the particle is ongoing). The fact that no particle corresponding to dark matter has been detected has two interpretations: the particle does not exist, or it interacts with measuring devices too weakly. Scientists may need to build bigger instruments or instruments that rely on different interactions (in the case that the particle is not a WIMP) before detection is possible. 
Other scientists are pursuing the idea of modifying General Relativity and looking for evidence of consistent discrepancies between relativity and the motion of astrophysical bodies that don't require custom fine-tuning at different size scales. Right now, different modifications are required for galaxies as opposed to clusters.
In fact, both dark matter and modified gravity have previous examples of being right.


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*Astronomical observations in the 1820s showed that Uranus was not moving in the way predicted by Newtonian gravity. The observed motion led to the conclusion that there was another planet whose gravity was affecting its motion. This planet, Neptune, was observed in 1846. Prior to its sighting, Neptune was dark matter: an unobserved mass whose gravity explained unpredicted motion of astronomical bodies.

*In the early 20th century, Mercury's motion was also found to contradict predictions based on Newtonian gravity. As was the case with Neptune, it was thought that another planet would be found inside Mercury's orbit. This planet (the dark matter) was named Vulcan. This planet was never found, and in fact, Mercury's motion required the development of General Relativity by Albert Einstein that modified Newton's theory of gravity. In this case, the purported dark matter did not exist, and our description of gravity had to be modified.
At present, it looks like dark matter is the more likely candidate to explain present discrepancies. More evidence is always coming in, and our understanding will eventually converge to one or the other or something completely different. Until then, all I can advise is patience.
A: If the only evidence for dark matter was from galactic rotation curves, a modification of gravity might be sufficient to explain the data. However we have lots of other evidence from astrophysics and cosmology for the existence of dark matter and a modification of gravity would not explain all of this evidence.
Here are some examples of the evidence:


*

*We can use gravitational lensing to measure the mass of dwarf
galaxies. These dwarf galaxies don't have many stars or molecular
clouds so the estimated mass from just ordinary matter would not
match the measured mass.

*In astrophysics, we need dark matter to be the seeds for the origins
of galaxies or else we cannot explain why we have so many galaxies. 
If dark matter did not exist galaxies would take too long to form.

*The Bullet Cluster is an example of the violent collision of two galaxy  clusters where the visible mass is quite
separated from the mass as measured by gravitational lensing.

*The very precise measurements of the patterns in the Cosmic Microwave
Background
(CMB) radiation by the WMAP and Plank satellites could not be
understood without dark matter. Note that at the time of the CMB there were no galaxies at all.

*The production and primordial abundance of Helium and Lithium in the Big Bang would not match observations without dark matter being present.


To explain all of this, all we have to do is to postulate of one additional stable particle that interacts very weakly with the other particles. Thus it's main interaction would only be gravitational. In theories that extend the Standard Model of particle physics, there are an abundance of possible kinds of particles that could be the dark matter particle. What we are missing is some direct experimental measurements of the dark matter particle properties such as mass and various interaction rates to decide between the many possible candidates. 
In fact there is really no reason to assume that there is only one dark matter particle - there could be a whole zoo of dark matter particles. According to all the evidence there is roughly 6 times as much dark matter as there is ordinary matter in our universe (as measured by comparing the total mass of the dark matter to the total mass of ordinary matter). Ordinary matter has a stable electron, proton, photon and three kinds of neutrinos. In addition you could consider each stable atomic element as another kind or particle. Then there are many dozens of unstable particles that will decay (eventually) to the stable particles. Since there is 6 times more dark matter than ordinary matter, maybe there are multiple (or many) kinds of stable dark matter particles. Having many different kinds of dark matter particles could be an easy explanation for why it has been so hard to detect and measure the properties of individual dark matter particles.
So the existence of dark matter is settled - it exists. What remains to be done is to measure the mass (or masses) and other properties of the one or more dark matter particles.
Most searches have only put limits on the mass and interaction strength of possible massive dark matter particles. However, another whole class of theoretically justified possible dark matter particles would be very low mass Axions; and there are not very strong experimental limits set on these candidates (yet). Finally, it might be possible that the dark matter particle does not interact with ordinary matter at all - except through gravitational effects. If dark matter only has gravitational interactions with ordinary matter we might never be able to determine the exact properties of the dark matter particle since we would never be able to detect it at all - only the collective gravitational effects of a large mass of dark matter particles could ever be measured.
You can see that there are plenty of explanations for why we have not yet been able to measure the properties of the dark matter particle(s). However, since modified gravity cannot explain all the astrophysical and cosmological evidence, dark matter particles must exist.
