Noether Currents and Maxwell-Type Equations of Motion in Higher Derivative Gravity Theories

In general coordinate invariant gravity theories whose Lagrangians contain arbitrarily high order derivative fields, the Noether currents for the global translation and for the Nakanishi’s IOSp(8|8) choral symmetry containing the BRS symmetry as its member are constructed. We generally show that for each of these Noether currents, a suitable linear combination of equations of motion can be brought into the form of a Maxwell-type field equation possessing the Noether current as its source term.

de Sitter spacetime with a Becchi–Rouet–Stora quartet

We generalize the topological model recently proposed and investigate the cosmological perturbations of the model. The model has an exact de Sitter background solution associated with the Becchi–Rouet–Stora (BRS) quartet terms which are regarded as the Lagrangian density of the topological field theory. The de Sitter solution can be selected without spontaneously breaking the BRS symmetry, and be interpreted as a gauge fixing of de Sitter spacetime. The BRS symmetry is preserved for the perturbations around the de Sitter background before we solve the constraints of general relativity. We derive action to the second-order of the perturbations and confirm that even after solving the constraints, we have the BRS symmetry at least for the second-order action. We construct the cosmological perturbation theory involving the BRS sector, and obtain the two-point correlation functions for the curvature perturbation and the isocurvature perturbations which compose the BRS sector. Our result gives a new description for de Sitter spacetime and the quantum field theory in de Sitter spacetime.

Some solutions for one of the cosmological constant problems

We propose several covariant models which may solve one of the problems in the cosmological constant. One of the models can be regarded as an extension of sequestering model. Other models could be regarded as extensions of the covariant formulation of the unimodular gravity. The contributions to the vacuum energy from the quantum corrections from the matters are absorbed into a redefinition of a scalar field and the quantum corrections become irrelevant to the dynamics. In a class of the extended unimodular gravity models, we also consider models which are regarded as topological field theories. The models can be extended and not only the vacuum energy but also any quantum corrections to the gravitational action could become irrelevant for the dynamics. We find, however, that the BRS symmetry in the topological field theories is broken spontaneously and therefore, the models might not be consistent.

EXTENDED BRS SYMMETRY IN TOPOLOGICAL FIELD THEORIES

A class of topological field theories like the BF model and Chern–Simons theory, when quantized in the Landau gauge, enjoys the property of invariance under a vector supersymmetry, which is responsible for their finiteness. We introduce a new type of gauge fixing which makes these theories invariant under an extended BRS symmetry, containing a new type of field, the ghost of diffeomorphisms. The presence of such an extension is naturally related to the vector supersymmetry discussed before.

EXACT SYMMETRIES REALIZED ON THE RG FLOW

We show that the BRS symmetry is present even with the finite IR cutoff in the Wilsonian RG approach. Based on the antifield formalism, we explain how the symmetry is realized on the RG flow.