In this paper, we study the various cylindrical solutions (cosmic strings) in gravity's rainbow scenario. In particular, we calculate the gravitational field equations corresponding to energy-dependent background. Further, we discuss the possible Kasner, quasi-Kasner and non-Kasner exact solutions of the field equations. In this framework, we find that quasiKasner solutions can not be realized in gravity's rainbow. Assuming only time-dependent metric functions, we also analyse the time-dependent vacuum cosmic strings in gravity's rainbow, which are completely different than the other GR solutions.
I. OVERVIEW AND MOTIVATIONA strong notion of an observer independent minimum length scale has been found in all theories of quantum gravity, for instance, in string theory [1], noncommutative geometry [2], loop quantum gravity [3,4] and Lorentzian dynamical triangulations [5][6][7][8]. Here we point out that the nascent GW astronomy [9] could help in discriminating among general relativity or alternative theories [10]. There is no harm to assume this minimum measurable length scale as the Planck scale. The mathematical ground of general theory of relativity is based on a smooth manifold which breaks down when energies of probe reaches the order of Planck energy [11,12].Keeping this point in mind, one may expect a radically new picture of spacetime, which includes departure from the standard relativistic dispersion relation. A departure from the standard dispersion relation indicates that the system incorporates a breaking of Lorentz invariance. * Electronic address: