According to Einstein's theory of relativity, the energy required to accelerate a particle to the limits of light-speed would be infinite. However, there is hypothesis suggesting that there might be a particle called Tachyons that only travel faster than the speed of light. This is a hypothesis because Tachyons do not exist in nature. And in science, everything has to exist in nature.
Quoting New Scientist
Source: Faster-than-light 'tachyons' might be impossible after all
Faster-than-light particles, or "tachyons", may be fundamentally impossible, according to two mathematical physicists. If they're right, their new theory would also imply that time - seemingly one of the most fundamental facets of nature - is no more than a mirage.
Although it is commonly believed that Einstein's theory of relativity says nothing can go faster than light, that is not quite true. Relativity does forbid ordinary matter from ever reaching the speed of light, because it would require infinite energy
But the theory does not rule out a realm of particles that can only travel faster than light. Named "tachyons" by physicists in the 1960s, these subatomic speedsters would actually need an infinite amount of energy to slow down to the crawl of light-speed.
Tachyons crop up as possibilities in several speculative physical theories, such as some versions of string theory. Physicists have searched for their expected signatures. If they are among the high-energy particles that hit Earth from space, tachyons would produce a signal similar to cosmic rays – except that they would reach ground-based detectors ahead of the secondary particles they created in the atmosphere.
No tachyons have ever been detected, however, and now James Wheeler and Joseph Spencer of Utah State University think they know why.
Wikipedia: Tachyon
A tachyon is any hypothetical particle that travels faster than light. Tachyonic fields have appeared theoretically in a variety of contexts, such as the Bosonic string theory. In the language of special relativity, a tachyon is a particle with space-like four-momentum and imaginary proper time. A tachyon is constrained to the space-like portion of the energy-momentum graph. Therefore, it cannot slow down to subluminal speeds. Even if tachyons were conventional, localisable particles, they would still preserve the basic tenets of causality in special relativity and not allow transmission of information faster than light, contrary to what has been written in many works of science fiction.