A review on extended special and general theory of relativity for superluminal particles and their cosmological applications

In the context of superluminal physics, this article explores the latest advancements including the primary theoretical developments in special and general theory of relativity (STR & GTR). We have reviewed the significant strides made so far and addressed the difficulties encountered with purported interpretation. The proposed or derived transformation factors for superluminal particles can be categorized into two categories, i.e., imaginary and real transformation factors. The transformation relations between the two classes of frames have been scrutinized using the metric expressions. The velocity addition and transformation relations of mass, momentum, and energy between the frames for superluminal particles have also been analyzed. The analyses using Klein-Gordon equation, which is the relativistic energy-momentum equation, for tachyons have been performed. In brane-antibrane system, universality of tachyon potential via tachyon condensation was articulated. The unstable brane system, by virtue of tachyon condensation, promotes the cosmological evidence. In advancing the pace of development of cosmological research, superluminal physics is one of the most astonishing fields. Approaching toward GTR for cosmological application, tachyons have been scrutinized in Schwarzschild, Kerr-Newman, and FLRW metric spaces. Tachyons in Friedman universe correspond to different applications, like measurements of Hubble's constant, theory of big-bang, expansion of universe. Some of the experimental evidences provided by GRS 1915+105, SN 1987A, GRB 030329, GW 170817, etc., for the existence of tachyons have also been analyzed. Einstein's postulate for the constancy of the speed of light has been commented on for the highest approachable speed observed by the particular observer.