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 Poincare 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.

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量子引力的现行代数公式及其在宇宙学中的应用

建立了基于当前代数的引力理论。规范原理而不是一般协方差与等价原理相结合在形式主义中起着举足轻重的作用，后者的原理是作为该理论的结果推导出来的。在这种方法中，结果证明衡量 Poincare 代数是不合适的，但衡量 $SO(N,M)$ 代数给出了一致的理论。这使得通过采用自旋连接和四分体场之间的关系可以具有反德西特和德西特时空。爱因斯坦方程是我们用自旋连接写成的基本引力方程的一部分。当这种形式主义应用于 $E(11)$ 代数时，其中三形式反对称张量是引力多重态的一部分，我们现在有一个基于 M 理论的代数引力理论，可以应用于经典极限的宇宙学。在不引入任何其他特设场的情况下，我们可以以早期“膨胀”宇宙的方式获得加速宇宙。