Emergent Spacetime and The Cosmological Constant

We address issues on the origin of gravity and the dark energy (or the cosmological constant) from the perspectives of emergent gravity. We discuss how the emergent gravity reveals a noble, radically different picture about the origin of spacetime, which is crucial for a tenable solution of the cosmological constant problem. In particular, the emergent gravity naturally explains the dynamical origin of flat spacetime, which is absent in Einstein gravity.Comment: 2 pages; Contribution to Proceedings of the workshop "Progress of String Theory and Quantum Field Theory", Osaka City University, Japan, 7-10 December 200

Mirror Symmetry in Emergent Gravity

Given a six-dimensional symplectic manifold $(M, B)$, a nondegenerate, co-closed four-form $C$ introduces a dual symplectic structure $\widetilde{B} = *C$ independent of $B$ via the Hodge duality $*$. We show that the doubling of symplectic structures due to the Hodge duality results in two independent classes of noncommutative U(1) gauge fields by considering the Seiberg-Witten map for each symplectic structure. As a result, emergent gravity suggests a beautiful picture that the variety of six-dimensional manifolds emergent from noncommutative U(1) gauge fields is doubled. In particular, the doubling for the variety of emergent Calabi-Yau manifolds allows us to arrange a pair of Calabi-Yau manifolds such that they are mirror to each other. Therefore, we argue that the mirror symmetry of Calabi-Yau manifolds is the Hodge theory for the deformation of symplectic and dual symplectic structures.Comment: v4; 20 pages, version to appear in Nucl. Phys.

Cosmic Inflation from Emergent Spacetime Picture

We argue that the emergent spacetime picture admits a background-independent formulation of cosmic inflation. The inflation in this picture corresponds to the dynamical emergence of spacetime while the conventional inflation is simply an (exponential) expansion of a preexisting spacetime owing to the vacuum energy carried by an inflaton field. We show that the cosmic inflation arises as a time-dependent solution of the matrix quantum mechanics describing the dynamical process of Planck energy condensate in vacuum without introducing any inflaton field as well as an {\it ad hoc} inflation potential. Thus the emergent spacetime picture realizes a background-independent description of the inflationary universe which has a sufficiently elegant and explanatory power to defend the integrity of physics against the multiverse hypothesis.Comment: 6 pages, 1 figure; Contribution to the Proceedings of the Second LeCosPA Symposium "Everything about Gravity", Taipei, 14-18 December, 201