Current Algebra Formulation of Quantum Gravity and Its Application to Cosmology

Gravity theory based on current algebra is formulated. The gauge principle rather than the general covariance combined with the equivalence principle plays the pivotal role in the formalism, and the latter principles are derived as a consequence of the theory. In this approach, it turns out that gauging the Poincar\'e algebra is not appropriate but gauging the $SO(N,M)$ algebra gives a consistent theory. This makes it possible to have Anti-de Sitter and de Sitter space-time by adopting a relation between the spin connection and the tetrad field. The Einstein equation is a part of our basic equation for gravity which is written in terms of the spin connection. When this formalism is applied to the $E(11)$ algebra in which the three-form antisymmetric tensor is a part of gravity multiplet, we have a current algebra gravity theory based on M-theory to be applied to cosmology in its classical limit. Without introducing any other ad-hoc field, we can obtain accelerating universe in the manner of the "inflating" universe at its early stage.