Doubly-Special Relativity is a new theory of special relativity first postulated in a paper by Giovanni Amelino-Camelia. In this theory, he postulates that in addition to the speed of light, a characteristic energy scale based on the Planck scale should remain invariant under relativistic transformations. There exist proposals that this theory may be related to loop quantum gravity.
One of the motivations for this work is the observation of high-energy cosmic rays that appear to violate the Greisen-Zatsepin-Kuzmin limit: the so-called GZK paradox.
Annotation for non-physicist readers: The theory is highly speculative as of first publishing in 2002. The author is respected by many and publishes in established journals, both on this and on related matters. The theory is built using a well established approach in theoretical physics named Invariance under transformation, which is colloquially (even in science) called relativistic. Nevertheless the theory is not considered a promising approach by a majority of members of the high-energy physics community.