Electromagnetic radiation allows us to see the universe. From radio waves as long as football fields, up through the colorful wavelengths of visible light and on to high powered x-rays and gamma rays, electromagnetic radiation is our principle tool for observation. Even when we switch to magnets or touch we've just swapped one form of electromagnetism for another.
What if some forms of matter don't react with electromagnetic radiation? A very clear plane of glass is transparent to the colors we see, but still opaque to other wavelengths. What if a structure was totally invisible? You could pass through it without ever knowing it was there. The only evidence would be the slight tug of gravity.
A globule of the stuff on Earth might evade detection forever, presumably drifting down into the molten core of the planet for an even better hiding spot. But on galactic scales the impact of the gravity would be visible on other matter. And astronomers have detected just that. Galaxies with insufficient mass to mathematically hold together do anyways. When you tally the things we see with the gravity we measure, they don't add up. Science has named this discrepancy dark matter. The leading candidate explanation right now is exotic particles that just don't react to light.
Einstein taught us that gravity is a distortion of spacetime by a massive object. The universe is like a trampoline: when something is placed on it, it bends the structure around it. Another object placed down will tend to roll towards the first object, obeying the attractive force of gravity (As an aside I've never really liked this way of explaining gravity. Why does the trampoline distort around an object? Gravity is pulling the object down towards the Earth, and the trampoline is in the way. We explain what gravity does by alluding to gravity).
There's an alternative explanation I've come up with. We see regular matter at the bottom of gravity wells, in exact proportions to the strength of the gravity, and as the matter moves the gravity does too. So we say that the matter distorts space, creating the gravity. What if that's backwards? What if spacetime is curved all on its own, and matter just pools in the low places? That is, what if protons, electrons and the whole gang don't bend space around them, just follow the existing grooves? You'd still see lots of matter in very dense places, but the cause and effect would be reversed. Gravitational distortions wouldn't follow a sun around, the sun would roll around to keep inside the distortion. Dark matter stops being a mysterious particle, and just becomes a gravity well that hasn't been totally filled.
Physical theories need tests. The most straightforward one I can think of is looking for cases where a massive body is caught in the grip of even larger one: A star passing by a black hole perhaps. If the gravity well travels too close to the blackhole, it may fall in. But if it skirts by its ever so closely, ejecting around the other side, the energy pooled in the star might fall in while the gravity well continued on its way. Dark matter being produced by super nova might also be a clue, with the great explosion ejecting mass from the gravity well. Finer measurements of gravity might allow us to use more practical sized objects.