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Register a new userKaluza-Klein Higher Derivative Induced Gravity
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Authors
W.F. Kao
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The existence and stability analysis of an inflationary solution in a $D+4$-dimensional anisotropic induced gravity is presented in this paper. Nontrivial conditions in the field equations are shown to be compatible with a cosmological model in which the 4-dimension external space evolves inflationary, while, the D-dimension internal one is static. In particular, only two additional constraints on the coupling constants are derived from the abundant field equations and perturbation equations. In addition, a compact formula for the non-redundant 4+D dimensional Friedmann equation is also derived for convenience. Possible implications are also discussed in this paper.
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Existence and stability analysis of the Kantowski-Sachs type inflationary universe in a higher derivative scalar-tensor gravity theory is studied in details. Isotropic de Sitter background solution is shown to be stable against any anisotropic perturbation during the inflationary era. Stability of the de Sitter space in the post inflationary era can also be realized with proper choice of coupling constants.
Motivated by the vast string landscape, we consider the shear viscosity to entropy density ratio in conformal field theories dual to Einstein gravity with curvature square corrections. After field redefinitions these theories reduce to Gauss-Bonnet gravity, which has special properties that allow us to compute the shear viscosity nonperturbatively in the Gauss-Bonnet coupling. By tuning of the coupling, the value of the shear viscosity to entropy density ratio can be adjusted to any positive value from infinity down to zero, thus violating the conjectured viscosity bound. At linear order in the coupling, we also check consistency of four different methods to calculate the shear viscosity, and we find that all of them agree. We search for possible pathologies associated with this class of theories violating the viscosity bound.
Stability analysis of the Kantowski-Sachs type universe in pure higher derivative gravity theory is studied in details. The non-redundant generalized Friedmann equation of the system is derived by introducing a reduced one dimensional generalized KS type action. This method greatly reduces the labor in deriving field equations of any complicate models. Existence and stability of inflationary solution in the presence of higher derivative terms are also studied in details. Implications to the choice of physical theories are discussed in details in this paper.
We study the membrane wrapping mode corrections to the Kaluza-Klein (KK) 6-brane in eleven dimensions. We examine the localized KK6-brane in the extended space in $E_{7(7)}$ exceptional field theory. In order to discuss the physical origin of the localization in the extended space, we consider a probe M2-brane in eleven dimensions. We show that a three-dimensional $mathcal{N} = 4$ gauge theory is naturally interpreted as a membrane generalization of the two-dimensional $mathcal{N} = (4,4)$ gauged linear sigma model for the fundamental string. We point out that the vector field in the $mathcal{N}= 4$ model is identified as a dual coordinate of the KK6-brane geometry. We find that the BPS vortex in the gauge theory gives rise to the violation of the isometry along the dual direction. We then show that the vortex corrections are regarded as an instanton effect in M-theory induced by the probe M2-brane wrapping around the M-circle.
We study teleparallel gravity in the emph{original} Kaluza-Klein (KK) scenario. Our calculation of the KK reduction of teleparallel gravity indicates that the 5-dimensional torsion scalar $^{(5)}T$ generates the non-Brans-Dicke type effective Lagrangian in 4-dimension due to an additional coupling between the derivative of the scalar field and torsion, but the result is equivalent to that in general relativity. We also discuss the cosmological behavior in the FLRW universe based on the effective teleparallel gravity.
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