Journal of the Korean Physical Society, Vol. 57, No. 3, September 2010, pp. 578∼581 Emergent Universe from Noncommutative Spacetime Jungjai Lee * Department of Physics, Daejin University, Pocheon 487-711 Hyun Seok Yang † Institute for the Early Universe, Ewha Womans University, Seoul 120-750 (Received 4 February 2010) The Big Bang, which was the birth of our Universe, happened at the Planck epoch. It was not an event that developed in a pre-existing space-time. Rather, it was a cosmological event simultaneously generating space-time as well as all other matter fields. Therefore, in order to describe the origin of our Universe, it is necessary to have a background-independent theory for quantum gravity in which no space-time structure is a priori assumed, but is defined from the theory. The emergent gravity based on noncommutative gauge theory provides such a background- independent formulation of quantum gravity, and the emergent space-time leads to a novel picture of the dynamical origin of space-time. We address some issues about the origin of our Universe and discuss the implications to cosmology of the emergent gravity. PACS numbers: 02.40.Gh, 11.10.Nx, 98.80.-k Keywords: Emergent gravity, Noncommutative space-time, Cosmology DOI: 10.3938/jkps.57.578 I. INTRODUCTION Gravity is a mysterious force. In Newtonian gravity, it is sourced by a mass m G . The fact that gravity is generated by a mass is a mundane feature also shared by other forces: an electric charge for the electromag- netic force, isospins for the weak force and color charges for the strong force. A mysterious and clandestine fea- ture of gravity now arises from the fact that the mass m G as a charge generating gravitational force, the so- called gravitational mass, is equal to the inertial mass m I appearing in the Newton’s law of motion, F = m I a. The equivalence principle stating that m G = m I implies that gravity can be interpreted as an inertial force and is clearly a universal force because every (massive) objects must satisfy the Newton’s law, F = m I a, so they must be subject to the gravitational force. Gravity influences and is influenced by everything that carries a mass. The importance of the equivalence principle was beau- tifully perceived by Einstein. He realized that it is always possible to locally eliminate gravitational force by a co- ordinate transformation, i.e., by a local inertial frame. That immediately leads to the remarkable picture that gravity has to describe a space-time geometry rather than a force immanent in space-time. Furthermore, it turns out that any object carrying an energy should feel * E-mail: jjlee@daejin.ac.kr † E-mail: hsyang@ewha.ac.kr the gravitational force; thus, even a massless particle, e.g., a photon, cannot be exempt from gravity because a massless particle cannot be at rest, but carries a definite momentum p or an energy E = |p|c. Before Einstein, space-time only served as a stage where physical events occurred. It never appeared as an actor. However, the equivalence principle again guar- antees the universality of gravity and, as coined by John A. Wheeler, the conspiracy between matters and gravity continues such that matter tells space-time how to curve, and space-time tells matter how to move. The spacetime, therefore, has to serve as a stage for the electromagnetic, the weak and the strong forces as well as an actor for the dynamical evolution of the stage (spacetime) itself. If gravity is a fundamental force as many still think, why is it so different from the other fundamental forces, and what is meant by the “fundamental”? We usually refer to a physical entity (force or field) as being “fundamental” when it does not have any super- ordinate substructure, but gravity reveals in many ways that it may not be a fundamental phenomenon in the above sense. It is quite amazing to notice that this pic- ture was already inherent in the Cartan formulation of gravity. -578-