Abstract
Abstract Gravity theory based on current algebra is formulated. The gauge principle rather than general covariance combined with the equivalence principle plays a 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 Poincaré 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 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 part of a gravity multiplet, we have a current algebra gravity theory based on M-theory in the sense that the internal group or the connection space representations of our model are those appearing in 11D supergravity. Moreover, when our formalism in its classical limit is applied to cosmology, by introducing conformal-like modes that connect the tetrad field/current and the spin connection field/current, we can obtain an accelerating universe in the manner of the “inflating” universe at its early stage.
Highlights
There is a long history of formulating gravity as a gauge theory starting from a pioneering work of Uchiyama [1].1 In many cases, such attempts start with the Einstein-Hilbert action and rewrite it in terms of spin connection and tetrad both of which are vector fields rather than tensor, making the theory a vector gauge theory
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
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
Summary
There is a long history of formulating gravity as a gauge theory starting from a pioneering work of Uchiyama [1].1 In many cases, such attempts start with the Einstein-Hilbert action and rewrite it in terms of spin connection and tetrad both of which are vector fields rather than tensor, making the theory a vector gauge theory. Since in writing Eq (7) we take the local Lorentz frame, it is intriguing that we can obtain Eq (10) that is automatically general covariant In this sense the general covariance is not an input of the theory but the consequence of the gauge principle formulated in the current algebra. Denote directions in the (N, 1) flat space-time When we discuss another algebra A where JμA includes higher-rank totally antisymmetric tensors, we can define them in a similar way. The significance of the Stelle-West ansatz [16] is that it gives the origin of the cosmological constant as the coefficient of the equation which relates the spin connection to the tetrad We will generalize this coefficient later as the time-dependent dynamical field and apply it to cosmology
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