We consider the evolution of the vacuum energy in the DGP model according to the holographic principle under the assumption that the relation linking the IR and UV cut-offs still holds in this scenario. The model is studied when the IR cut-off is chosen to be the Hubble scale H −1 , the particle horizon R ph and the future event horizon R eh , respectively. And the two branches of the DGP model are also taken into account. Through numerical analysis, we find that in the cases of H −1 in the (+) branch and R eh in both branches, the vacuum energy can play the role of dark energy. Moreover, when considering the combination of the vacuum energy and the 5D gravity effect in both branches, the equation of state of the effective dark energy may cross −1, which may lead to the Big Rip singularity. Besides, we constrain the model with the Type Ia supernovae and baryon oscillation data and find that our model is consistent with current data within 1σ, and that the observations prefer either a pure holographic dark energy or a pure DGP model. 98.80.Es; 95.36.+x

Recent developments have revealed a new phenomenon, i.e. the residues of the poles of the holographic retarded two point functions of generic operators vanish at certain complex values of the frequency and momentum. This so-called pole-skipping phenomenon can be determined holographically by the near horizon dynamics of the bulk equations of the corresponding fields. In particular, the pole-skipping point in the upper half plane of complex frequency has been shown to be closed related to many-body chaos, while those in the lower half plane also places universal and nontrivial constraints on the two point functions. In this paper, we study the effect of higher curvature corrections, i.e. the stringy correction and Gauss-Bonnet correction, to the (lower half plane) pole-skipping phenomenon for generic scalar, vector, and metric perturbations. We find that at the poleskipping points, the frequencies ω n = −i2πnT are not explicitly influenced by both R 2 and R 4 corrections, while the momenta k n receive corresponding corrections.H. Corrections to k 1 in three channels of metric perturbations 30 -2 -Recently, the near horizon analysis is generalized in [17] to equations of bulk fields dual to spin-0, spin-1 and spin-2 operators, and pole-skipping is found to exist in retarded two point functions of these operators. However, these pole-skipping points appear in the lower half plane of the complex frequency, in contrast to the aforementioned pole-skipping point of chaos located in the upper half plane at ω = +i2πT . This indicates that pole-skipping may not always be directly related to quantum chaos, but could be a consequence of a more general feature of near horizon bulk equations. Relevant discussions can also be found in [18,19,20].where A and B are coefficients in the asymptotic expansion of the scalar field near the boundary φ → Ar ∆−4 + Br −∆ .(2.5) 2 In this paper, the AdS radius is always set to unity for convenience. 3 One may well consider the equivalent form ∇µ∇ µ ϕ − m 2 ϕ = 0. Note in that case, the near horizon expansion of the perturbation equation would in general be different at each order due to the extra √ −g factor. Of course, the physics will remain the same. Here we simply follow the convention used in [17] for the sake of comparison.11 Note that at λGB = 1/4, N 2 GB = 1/2, the shear viscosity vanishes, and the theory exhibits unusual properties in many aspects, such as quasinormal modes and thermodynamics, see [54,59,60] for detailed discussions. Since this value lies far outside of the causality range (4.3), we will not consider it in the following.

As a spacetime with compact spatial sections, de Sitter spacetime does not have a de Sitter-invariant ground state for a minimally-coupled massless scalar field that gives definite expectation values for any observables not invariant under constant shifts of the field. However, if one restricts to observables that are shift invariant, as the action is, then there is a unique vacuum state. Here we calculate the shift-invariant four-point function that is the vacuum expectation value of the product of the difference of the field values at one pair of points and of the difference of the field values at a second pair of points. We show that this vacuum expectation value obeys a cluster-decomposition property of vanishing in the limit that the one pair of points is moved arbitrarily far from the other pair. We also calculate the shift-invariant correlation of the gradient of the scalar field at two different points and show that it also obeys a cluster-decomposition property. Possible relevance to a putative de Sitter-invariant quantum state for gravity is discussed. * Alberta- Thy-6-12, arXiv:1204.4462 [hep-th] † Internet address:

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Abstract:We use the method of evaluating the decay rate in terms of the imaginary part of a probe brane action to study the holographic Schwinger effect. In the confining D3-branes case, we find that the Schwinger effect occurs at energy scales higher than the Kaluza-Klein mass, indicating the absence of such effect when the dual gauge field theory can be regarded as an 2+1 dimensional theory. This property is independent of the configuration of the probe brane. In the case of D3-branes with a B field dual to a noncommutative super Yang-Mills theory, we study how the decay rate is affected by the noncommutative effect.