These objects are sometimes called tardyons. In order for something to travel at the speed of light it would have to have an imaginary number for its mass. An imaginary number is a number that is a multiple of the square root of a negative number. There have been a few experiments to find tachyons using a detector called a cerenkov detector. This detector is able to measure the speed of a particle traveling through a medium.
Photons travel at a slower speed inside a medium.
If a particle travels though a medium at a speed that is greater than light for that medium cerenkov radiation occurs. This is analogous to the sonic boom produced when an airplane travels faster than the speed of sound in air or the shock wave at the bow of a ship. If tachyons existed you would be able to see cerenkov radiation in a vacuum. A few cerenkov experiments were conducted in a vacuum and no radiation was found, so it is generally accepted that tachyons do no exist. I hope this helped you.