EJTP 12, No. IYL15-34 (2015) 173–182 Electronic Journal of Theoretical Physics The Eternal Rainbow Universe Ahmed Farag Ali 1∗ and Barun Majumder 2† 1 Department of Physics, Faculty of Sciences, Benha University, Benha, 13518, Egypt 2 Indian Institute of Technology Gandhinagar, Ahmedabad, Gujarat 382424, India Received 10 November 2015, Accepted 25 November 2015, Published 15 December 2015 Abstract: There are many strong theoretical motivations on why there can be a Lorentz invariance violation due to quantum gravity effects at length scales of the order of Planck length. In this present study, we consider some theoretical arguments which either favors the idea of Lorentz invariance violation or modifies the action of the Lorentz group acting on momentum space. All these ideas predicts a modification in the dispersion relation that depends on some functions known as Rainbow functions. With simple calculations and arguments we show that there are some unique choices of the Rainbow functions which predict an infinitely existing universe near the Plank scale and hence resolve the big bang singularity. c  Electronic Journal of Theoretical Physics. All rights reserved. Keywords: Lorentz Invariance Violation; Rainbow Functions; Eternal Rainbow Universe; Big Bang Theory; Quantum Gravity PACS (2010): 04.60.-m; 11.30.Cp; 98.80.Bp; 98.80.-k Einstein’s general theory of relativity is by far the most successful theory in describing the universe on a macroscopic scale. The classical theory is well tested in the weak field regime but essentially breaks down in the regime where it predicts singularities, beyond which the classical notion of spacetime cannot be extended [1]. For example, the big bang singularity appears in almost all the cosmological models which are exact solutions of Einstein’s equations subject to some symmetries. At the singularity the classical theory breaks down as curvatures diverge and we believe that some profound quantum theory of gravity should replace the classical theory at these scales. There are several approaches or proposals for a complete quantum theory of gravity and the common feature among them is the existence of a minimum measurable length scale which is the Planck length. This minimal length is expected to play the role of a natural cut-off and resolve the curvature singularities that exists in the classical theory. Any quantum theory of gravity is expected to induce Lorentz invariance violation at Planck scale. This is due to the fact ∗ Email: ahmed.ali@fsc.bu.edu.eg † Email: barunbasanta@iitgn.ac.in