Not everyone is sold on dark matter, not by a long shot. A few astronomers believe that the laws of motion and gravity, formulated by Newton and expanded by Einstein, may have finally met their match. If that's the case, then a modification of gravity, not some unseen particle, could explain the effects attributed to dark matter.
In the 1980s, physicist Mordehai Milgrom suggested that Newton's second law of motion (force = mass x acceleration, f = ma) should be reexamined in the cases of galactic motions. His basic idea was that at very low accelerations, corresponding to large distances, the second law broke down. To make it work better, he added a new mathematical constant into Newton's famous law, calling the modification MOND, or Modified Newtonian Dynamics. Because Milgrom developed MOND as a solution to a specific problem, not as a fundamental physics principle, many astronomers and physicists have cried foul.
Also, MOND can't account for evidence of dark matter discovered by other techniques that don't involve Newton's second law, such as X-ray astronomy and gravitational lenses. A 2004 revision to MOND, known as TeVeS (Tensor-Vector-Scalar gravity), introduces three different fields into space-time to replace the one gravitational field. Because TeVeS incorporates relativity, it can accommodate phenomena such as lensing. But that didn't settle the debate. In 2007, physicists tested Newton's second law down to accelerations as low as 5 x 10-14 m/s2 and reported that f = ma holds true with no necessary modifications (see American Institute of Physics News Update: "Newton's Second Law of Motion," April 11, 2007), making MOND seem even less attractive.
Still other alternatives regard dark matter as an illusion resulting from quantum physics. In 2011, Dragan Hajdukovic at the European Organization for Nuclear Research (CERN) proposed that empty space is filled with particles of matter and antimatter that are not only electrical opposites, but also gravitational opposites. With different gravitational charges, the matter and antimatter particles would form gravitation dipoles in space. If these dipoles formed near a galaxy – an object with a massive gravitational field – the gravitational dipoles would become polarized and strengthen the galaxy's gravitational field. This would explain the gravitational effects of dark matter without requiring any new or exotic forms of matter.