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Register a new userCorrections to de Sitter entropy through holography
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Nikolaos Tetradis
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The holographic entanglement entropy is computed for an entangling surface that coincides with the horizon of a boundary de Sitter metric. This is achieved through an appropriate slicing of anti-de Sitter space and the implementation of a UV cutoff. The entropy is equal to the Wald entropy for an effective action that includes the higher-curvature terms associated with the conformal anomaly. The UV cutoff can be expressed in terms of the effective Planck mass and the number of degrees of freedom of the dual theory. The entanglement entropy takes the expected form of the de Sitter entropy, including logarithmic corrections.
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We review the results of refs. [1,2], in which the entanglement entropy in spaces with horizons, such as Rindler or de Sitter space, is computed using holography. This is achieved through an appropriate slicing of anti-de Sitter space and the implementation of a UV cutoff. When the entangling surface coincides with the horizon of the boundary metric, the entanglement entropy can be identified with the standard gravitational entropy of the space. For this to hold, the effective Newtons constant must be defined appropriately by absorbing the UV cutoff. Conversely, the UV cutoff can be expressed in terms of the effective Planck mass and the number of degrees of freedom of the dual theory. For de Sitter space, the entropy is equal to the Wald entropy for an effective action that includes the higher-curvature terms associated with the conformal anomaly. The entanglement entropy takes the expected form of the de Sitter entropy, including logarithmic corrections.
In the setup of ghost condensation model the generalized second law of black hole thermodynamics can be respected under a radiatively stable assumption that couplings between the field responsible for ghost condensate and matter fields such as those in the Standard Model are suppressed by the Planck scale. Since not only black holes but also cosmology are expected to play important roles towards our better understanding of gravity, we consider a cosmological setup to test the theory of ghost condensation. In particular we shall show that the de Sitter entropy bound proposed by Arkani-Hamed, et.al. is satisfied if ghost inflation happened in the early epoch of our universe and if there remains a tiny positive cosmological constant in the future infinity. We then propose a notion of cosmological Page time after inflation.
Demanding $O(d,d)$-duality covariance, Hohm and Zwiebach have written down the action for the most general cosmology involving the metric, $b$-field and dilaton, to all orders in $alpha$ in the string frame. Remarkably, for an FRW metric-dilaton ansatz the equations of motion turn out to be quite simple, except for the presence of an unknown function of a single variable. If this unknown function satisfies some simple properties, it allows de Sitter solutions in the string frame. In this note, we write down the Einstein frame analogues of these equations, and make some observations that make the system tractable. Perhaps surprisingly, we find that a necessary condition for de Sitter solutions to exist is that the unknown function must satisfy a certain second order non-linear ODE. The solutions of the ODE do not have a simple power series expansion compatible with the leading supergravity expectation. We discuss possible interpretations of this fact. After emphasizing that all (potential) string and Einstein frame de Sitter solutions have a running dilaton, we write down the most general cosmologies with a constant dilaton in string/Einstein frame: these have power law scale factors.
We outline a program for interpreting the higher-spin dS/CFT model in terms of physics in the causal patch of a dS observer. The proposal is formulated in elliptic de Sitter space dS_4/Z_2, obtained by identifying antipodal points in dS_4. We discuss recent evidence that the higher-spin model is especially well-suited for this, since the antipodal symmetry of bulk solutions has a simple encoding on the boundary. For context, we test some other (free and interacting) theories for the same property. Next, we analyze the notion of quantum field states in the non-time-orientable dS_4/Z_2. We compare the physics seen by different observers, with the outcome depending on whether they share an arrow of time. Finally, we implement the marriage between higher-spin holography and observers in dS_4/Z_2, in the limit of free bulk fields. We succeed in deriving an observers operator algebra and Hamiltonian from the CFT, but not her S-matrix. We speculate on the extension of this to interacting higher-spin theory.
In this work we analyze the role of $alpha $-corrections to type IIB orientifold compactifications in Kahler moduli stabilization and inflation. In particular, we propose a model independent scenario to achieve non-supersymmetric Minkowski and de Sitter vacua for geometric backgrounds with positive Euler-characteristic and generic number of Kahler moduli. The vacua are obtained by a tuning of the flux superpotential. Moreover, in the one-modulus case we argue for a mechanisms to achieve model independent slow-roll.
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