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Register a new userBackreaction effects due to matter coupled higher derivative gravity
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AdS-hydrodynamics has proven to be a useful tool for obtaining transport coefficients observed in the collective flow of strongly coupled fluids like quark gluon plasma (QGP). Particularly, the ratio of shear viscosity to entropy density ${eta/ s}$ obtained from elliptic flow measurements can be matched with the computation done in the dual gravity theory. The experimentally observed temperature dependence of ${eta/ s}$ requires the study of scalar matter coupled AdS gravity including higher derivative curvature corrections. We obtain the backreaction to the metric for such a matter coupled AdS gravity in $D$-dimensional spacetime due to the higher derivative curvature corrections. Then, we present the backreaction corrections to shear-viscosity $eta$ and entropy density $s$.
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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.
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 holographic shear sum rules in Einstein gravity with curvature squared corrections. Sum rules relate weighted integral over spectral densities of retarded correlators in the shear channel to the one point functions of the CFTs. The proportionality constant can be written in terms of the data of three point functions of the stress tenors of the CFT ($t_2$ and $t_4$). For CFTs dual to two derivative Einstein gravity, this proportionality constant is just $frac{d}{2(d+1)}$. This has been verified by a direct holographic computation of the retarded correlator for Einstein gravity in $AdS_{d+1}$ black hole background. We compute corrections to the holographic shear sum rule in presence of higher derivative corrections to the Einstein-Hilbert action. We find agreement between the sum rule obtained from a general CFT analysis and holographic computation for Gauss Bonnet theories in $AdS_5$ black hole background. We then generalize the sum rule for arbitrary curvature squared corrections to Einstein-Hilbert action in $dgeq 4$. Evaluating the parameters $t_2$ and $t_4$ for the possible dual CFT in presence of such curvature corrections, we find an agreement with the general field theory derivation to leading order in coupling constants of the higher derivative terms.
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