Dynamical dark energy with a constant vacuum energy density

We present a holographic dark-energy model in which the Newton constant $G_{N}$ scales in such a way as to render the vacuum energy density a true constant. Nevertheless, the model acts as a dynamical dark-energy model since the scaling of $G_{N}$ goes at the expense of deviation of concentration of dark-matter particles from its canonical form and/or of promotion of their mass to a time-dependent quantity, thereby making the effective equation of state (EOS) variable and different from -1 at the present epoch. Thus the model has a potential to naturally underpin Dirac's suggestion for explaining the large-number hypothesis, which demands a dynamical $G_{N}$ along with the creation of matter in the universe. We show that with the aid of observational bounds on the variation of the gravitational coupling, the effective-field theory IR cutoff can be strongly restricted, being always closer to the future event horizon than to the Hubble distance. As for the observational side, the effective EOS restricted by observation can be made arbitrary close to -1, and therefore the present model can be considered as a ``minimal'' dynamical dark-energy scenario. In addition, for nonzero but small curvature (|\Omega_{k0}| \lsim 0.003), the model easily accommodates a transition across the phantom line for redshifts z \lsim 0.2 , as mildly favored by the data. A thermodynamic aspect of the scenario is also discussed.Comment: 14 pages, 2 figures, revised, title modified, references added, to appear in Phys. Lett.

Stability of Horava-Lifshitz Black Holes in the Context of AdS/CFT

The anti--de Sitter/conformal field theory (AdS/CFT) correspondence is a powerful tool that promises to provide new insights toward a full understanding of field theories under extreme conditions, including but not limited to quark-gluon plasma, Fermi liquid and superconductor. In many such applications, one typically models the field theory with asymptotically AdS black holes. These black holes are subjected to stringy effects that might render them unstable. Ho\v{r}ava-Lifshitz gravity, in which space and time undergo different transformations, has attracted attentions due to its power-counting renormalizability. In terms of AdS/CFT correspondence, Ho\v{r}ava-Lifshitz black holes might be useful to model holographic superconductors with Lifshitz scaling symmetry. It is thus interesting to study the stringy stability of Ho\v{r}ava-Lifshitz black holes in the context of AdS/CFT. We find that uncharged topological black holes in $\lambda=1$ Ho\v{r}ava-Lifshitz theory are nonperturbatively stable, unlike their counterparts in Einstein gravity, with the possible exceptions of negatively curved black holes with detailed balance parameter $\epsilon$ close to unity. Sufficiently charged flat black holes for $\epsilon$ close to unity, and sufficiently charged positively curved black holes with $\epsilon$ close to zero, are also unstable. The implication to the Ho\v{r}ava-Lifshitz holographic superconductor is discussed.Comment: 15 pages, 6 figures. Updated version accepted by Phys. Rev. D, with corrections to various misprints. References update

The Holographic Principle for General Backgrounds

We aim to establish the holographic principle as a universal law, rather than a property only of static systems and special space-times. Our covariant formalism yields an upper bound on entropy which applies to both open and closed surfaces, independently of shape or location. It reduces to the Bekenstein bound whenever the latter is expected to hold, but complements it with novel bounds when gravity dominates. In particular, it remains valid in closed FRW cosmologies and in the interior of black holes. We give an explicit construction for obtaining holographic screens in arbitrary space-times (which need not have a boundary). This may aid the search for non-perturbative definitions of quantum gravity in space-times other than AdS.Comment: 15 pages, 4 figures. Based on a talk given at Strings '99. Includes a reply to recent criticism. For more details, examples, and references, see hep-th/9905177 and hep-th/990602

Holography and entropy bounds in the plane wave matrix model

As a quantum theory of gravity, Matrix theory should provide a realization of the holographic principle, in the sense that a holographic theory should contain one binary degree of freedom per Planck area. We present evidence that Bekenstein's entropy bound, which is related to area differences, is manifest in the plane wave matrix model. If holography is implemented in this way, we predict crossover behavior at strong coupling when the energy exceeds N^2 in units of the mass scale.Comment: 19 pages; v2: references adde

Brick Walls and AdS/CFT

We discuss the relationship between the bulk-boundary correspondence in Rehren's algebraic holography (and in other 'fixed-background' approaches to holography) and in mainstream 'Maldacena AdS/CFT'. Especially, we contrast the understanding of black-hole entropy from the viewpoint of QFT in curved spacetime -- in the framework of 't Hooft's 'brick wall' model -- with the understanding based on Maldacena AdS/CFT. We show that the brick-wall modification of a Klein Gordon field in the Hartle-Hawking-Israel state on 1+2-Schwarzschild AdS (BTZ) has a well-defined boundary limit with the same temperature and entropy as the brick-wall-modified bulk theory. One of our main purposes is to point out a close connection, for general AdS/CFT situations, between the puzzle raised by Arnsdorf and Smolin regarding the relationship between Rehren's algebraic holography and mainstream AdS/CFT and the puzzle embodied in the 'correspondence principle' proposed by Mukohyama and Israel in their work on the brick-wall approach to black hole entropy. Working on the assumption that similar results will hold for bulk QFT other than the Klein Gordon field and for Schwarzschild AdS in other dimensions, and recalling the first author's proposed resolution to the Mukohyama-Israel puzzle based on his 'matter-gravity entanglement hypothesis', we argue that, in Maldacena AdS/CFT, the algebra of the boundary CFT is isomorphic only to a proper subalgebra of the bulk algebra, albeit (at non-zero temperature) the (GNS) Hilbert spaces of bulk and boundary theories are still the 'same' -- the total bulk state being pure, while the boundary state is mixed (thermal). We also argue from the finiteness of its boundary (and hence, on our assumptions, also bulk) entropy at finite temperature, that the Rehren dual of the Maldacena boundary CFT cannot itself be a QFT and must, instead, presumably be something like a string theory.Comment: 54 pages, 3 figures. Arguments strengthened in the light of B.S. Kay `Instability of Enclosed Horizons' arXiv:1310.739

The paradigm of the area law and the structure of transversal and longitudinal lightfront degrees of freedom

It is shown that an algebraically defined holographic projection of a QFT onto the lightfront changes the local quantum properties in a very drastic way. The expected ubiquitous vacuum polarization characteristic of QFT is confined to the lightray (longitudinal) direction, whereas operators whose localization is transversely separated are completely free of vacuum correlations. This unexpected ''transverse return to QM'' combined with the rather universal nature of the strongly longitudinal correlated vacuum correlations (which turn out to be described by rather kinematical chiral theories) leads to a d-2 dimensional area structure of the d-1 dimensional lightfront theory. An additive transcription in terms of an appropriately defined entropy related to the vacuum restricted to the horizon is proposed and its model independent universality aspects which permit its interpretation as a quantum candidate for Bekenstein's area law are discussed. The transverse tensor product foliation structure of lightfront degrees of freedom is essential for the simplifying aspects of the algebraic lightcone holography. Key-words: Quantum field theory; Mathematical physics, Quantum gravityComment: 16 pages latex, identical to version published in JPA: Math. Gen. 35 (2002) 9165-918