6059 10.1140/epjc/s10052-018-6059-7 587 56 Loop quantum cosmology with a non-commutative quantum deformed photon gas Regular Article - Theoretical Physics 1 25 2018 7 11 2018 6 8 2018 7 9 2018 7 20 The Author(s) 2018 Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. Funded by SCOAP3 Yunxin Ye yeyunxin96@hotmail.com Tiberiu Harko t.harko@ucl.ac.uk Shi-Dong Liang stslsd@mail.sysu.edu.cn 0000 0001 2360 039X grid.12981.33 School of Physics Sun Yat-Sen University Guangzhou 510275 People’s Republic of China 0000 0004 1937 1397 grid.7399.4 Department of Physics Babes-Bolyai University Kogalniceanu Street 400084 Cluj-Napoca Romania 0000000121901201 grid.83440.3b Department of Mathematics University College London Gower Street London WC1E 6BT UK 0000 0001 2360 039X grid.12981.33 State Key Laboratory of Optoelectronic Material and Technology, and Guangdong Province Key Laboratory of Display Material and Technology Sun Yat-Sen University Guangzhou 510275 People’s Republic of China Abstract The non-commutativity of the space-time had important implications for the very early Universe, when its size was of the order of the Planck length. An important implication of this effect is the deformation of the standard dispersion relation of special relativity. Moreover, in the Planck regime gravity itself must be described by a quantum theory. We consider the implications of the modified dispersion relations for a photon gas, filling the early Universe, in the framework of loop quantum cosmology, a theoretical approach to quantum gravity. We consider three types of deformations of the dispersion relations of the photon gas, from which we obtain the Planck scale corrections to the energy density and pressure. The cosmological implications of the modified equations of state are explored in detail for all radiation models in the framework of the modified Friedmann equation of loop quantum cosmology. By numerically integrating the evolution equations we investigate the evolution of the basic cosmological parameters (scale factor, Hubble function, radiation temperature, and deceleration parameter) for a deformed photon gas filled Universe. In all models the evolution of the Universe shows the presence of a (nonsingular) bounce, corresponding to the transition from a contracting to an expanding phase.