Astronomy has come a long way in the last two thousand years. It wasn’t all that long ago that our ancestors looked up at the night sky and worshiped the stars as Gods. Now, we know that stellar objects are actually massive accumulations of gas and dust, and that many of the shining objects we see in the sky are not even stars, but other planets and distant galaxies. These new understandings have brought us a long way towards understanding the cosmos. But of course, there are still some things that we haven’t quite figured out.
One of the greatest mysteries of astronomy is the problem of the missing universe. Well, the universe isn’t exactly missing, but a lot of its mass is. Ultimately, all of the matter scientists can see in the universe accounts for only a small percent of the observed gravity. Everything on Earth, everything we’ve ever observed with our instruments, all normal matter—it all adds up to less than 5% of the Universe. Essentially, some unobservable something in influencing the motions of the cosmos.
Astronomers often use dark matter to explain this missing matter. However, the dark matter interactions that scientists believe they observed remain inconclusive. Thus, scientists have yet to definitively determine that dark matter exists. In fact, we may never actually be able to detect it... and it isn't ideal at predicting all manner of situations. As you see, dark matter does have some problems.
Some researchers think that the problem is really our understanding of gravity. In order to explain why the universe seems to behave as if there's so much more matter in it, some scientists advocate MOND (Modified Theory of Newtonian Dynamics) instead of dark matter.
In short, MOND is a classical dynamics theory which explains the mass discrepancies in galactic systems without invoking dark entities (like dark matter or dark energy). To accomplish this, MOND introduces a new universal constant of nature with the dimension of acceleration. Under MOND, mass is much more effective at bending space-time than under General Relativity, so it takes less stuff in the universe to account for all the gravity we measure.
So, how does it work? MOND can be interpreted as either a modification of gravity, or as a modification of inertia through a breaking of the equivalence of inertial and gravitational mass. The modification occurs at very small accelerations. Above a critical acceleration (the one parameter of the theory), everything is normal. Below the critical acceleration, General Relativity does not hold. In essence, General Relativity and MOND apply in very different regimes. The two regimes are joined smoothly by an interpolation function (to see the equation, check the sources section).
But MOND doesn’t solve all the problems. To make MOND work for clusters, it must include more complicated concepts, such as entities called dark fields, which work in a similar way as dark matter in order to alter the amount of gravity present. So many argue that MOND doesn’t actually solve any problems, just create new ones. There are other issues with the concept, but for the sake of brevity, they are just sourced.
Altering such a fundamental law like General Relativity is, obviously, rather drastic. However, MOND advocates respond by noting that it is “just as drastic to fill the universe with non-baryonic cold dark matter consisting of new fundamental particles we don't actually know to exist.”
Either way, we are missing something fundamental about the nature of our universe, and more study is needed to determine what this something is--Dark matter, MOND, or something else entirely.