We can consider a quintom model of dark energy with non-minimal coupling between scalar field and modified gravity. The Lagrangian for scalar field can be inspired by tachyonic lagrangian in string theory....
In special relativity, a faster-than-light particle would have space-like momentum, in contrast to ordinary particles that have time-like four-momentum. It would also have imaginary mass. Being constrained to the space-like portion of the energy–momentum graph, it could not slow down to subluminal speeds. Most physicists think that faster-than-light particles cannot exist because they are not consistent with the known laws of physics. If such particles did exist, they could be used to build a tachyonic antitelephone and send signals faster than light, which (according to special relativity) would lead to violations of causality. Potentially consistent theories that allow faster-than-light particles include those that break Lorentz invariance, the symmetry underlying special relativity, so that the speed of light is not a barrier.
A tachyon, It is a hypothetical subatomic particle that moves faster than light. A tachyon is a particle with space-like 4-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.
In the framework of quantum field theory, tachyons are understood as signifying an instability of the system and treated using tachyon condensation, rather than as real faster-than-light particles, and such instabilities are described by tachyonic fields. Tachyonic fields have appeared theoretically in a variety of contexts, such as the bosonic string theory.
According to the contemporary and widely accepted understanding of the concept of a particle, tachyon particles are too unstable to be treated as existent. By that theory, faster than light information transmission and causality violation with tachyons are impossible. No experimental evidence for the existence of tachyon particles has been found. In the 1967 paper that coined the term,[1] Feinberg proposed that tachyonic particles could be quanta of a quantum field with negative squared mass. However, it was soon realized that excitations of such imaginary mass fields do not in fact propagate faster than light,[4] and instead represent an instability known as tachyon condensation.[2] Nevertheless, negative squared mass fields are commonly referred to as "tachyons",[5] and in fact have come to play an important role in modern physics.
References:
[1] https://www.princeton.edu/~achaney/tmve/wiki100k/docs/Tachyon.html
[2] http://www.physics.ox.ac.uk/Users/Gabella/images/tachyons.pdf
[3] http://en.wikipedia.org/wiki/Tachyon#Tachyons_in_string_theory
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