Constraining Lorentz Invariance Violation Via Cosmography

Lorentz Invariance(LI)is the cornerstone for both special realtivity and standard model of particle physcics.Specifically the physics is invariant under transformation between any two inertial restframes guaranteed by LI,at the same time LI is also one of the basic assumptions of CPT theorem which plays an important role in particle physics.As we all known,the theory of relativity has been well tested,through observations from gravitational redshift,bending of ligh,precession of perihelion of Mercury and so on.The same cases is for standard model of particle physics for the discovery of the 125 GeV higgs boson.So it seem that LI is truly reliable as it is.However,It is not always the cases that LI holds forever(LIV),under the framework of certain quantum gravity or planck scale physics,LI may be violated,which will have a great impact on the two pillars of modern physics mentioned above.Therefore,observationally testing LI is a big topic of modern physics.Once LIV,a quantumized dispersion of relations for photons may be predicted,the velocity of light will be energy dependent instead of as a contant.But as the energy scale of LIV is high enough so that the variance of velocity of photons is too subtle to be grasped.Luckily,Gama Ray Burst(GRB)sources kMpc away from us amplify that so much that we could have chances to observatinally test the tiny effect.When constraining LIV,the expansion history of our universe is needed,which can be given by specified cosmological models.As a consequence,the result about LIV is model dependent,namely,the result is not general and reliable enough unless every specified cosmological models are considered that we may dead tired.Cosmography as a powerful tool to describe the expansion history of our universe may save us at this moment,which only rely on cosmological principles,neither the energy components of our universe nor any theory of graviton.So the result is reliable and general if we just use cosmograhy instead of any specified cosmogical models to describe the expansion history of our universe when constraining LIV.In the present paper,LIV are constrained from the cosmic observations which include timelags data from GRB photons,supernova samples of JLA and baryon acoustic oscillation(BAO)using cosmography rather than any specified models describing the expansion history of our universe.It is noted that by using Markov Chain Monte Carlo(MCMC)method,we find that current data possibly indicates soft LIV signatures.