Geometric and Renormalized Entropy in Conformal Field Theory

In statistical physics, useful notions of entropy are defined with respect to some coarse graining procedure over a microscopic model. Here we consider some special problems that arise when the microscopic model is taken to be relativistic quantum field theory. These problems are associated with the existence of an infinite number of degrees of freedom per unit volume. Because of these the microscopic entropy can, and typically does, diverge for sharply localized states. However the difference in the entropy between two such states is better behaved, and for most purposes it is the useful quantity to consider. In particular, a renormalized entropy can be defined as the entropy relative to the ground state. We make these remarks quantitative and precise in a simple model situation: the states of a conformal quantum field theory excited by a moving mirror. From this work, we attempt to draw some lessons concerning the ``information problem'' in black hole physicsComment: 35 pages, 4 figures available on request to [email protected], use Phyzzx, PUPT-1454, IASSNS-HEP 93/8

Conformal relativity versus Brans-Dicke and superstring theories

Conformal relativity theory which is also known as Hoyle-Narlikar theory has recently been given some new interest. It is an extended relativity theory which is invariant with respect to conformal transformations of the metric. In this paper we show how conformal relativity is related to the Brans-Dicke theory and to the low-energy-effective superstring theory. We show that conformal relativity action is equaivalent to a transformed Brans-Dicke action for Brans-Dicke parameter $\omega = -3/2$ in contrast to a reduced (graviton-dilaton) low-energy-effective superstring action which corresponds to a Brans-Dicke action with Brans-Dicke parameter $\omega = -1$. In fact, Brans-Dicke parameter $\omega =-3/2$ gives a border between a standard scalar field evolution and a ghost. We also present basic cosmological solutions of conformal relativity in both Einstein and string frames. The Eintein limit for flat conformal cosmology solutions is unique and it is flat Minkowski space. This requires the scalar field/mass evolution instead of the scale factor evolution in order to explain cosmological redshift. It is interesting that like in ekpyrotic/cyclic models, a possible transition through a singularity in conformal cosmology in the string frame takes place in the weak coupling regime.Comment: REVTEX4, 12 pages, an improved version, references adde

Anomaly-Induced Effective Action and Inflation

In the early Universe matter can be described as a conformal invariant ultra-relativistic perfect fluid, which does not contribute, on classical level, to the evolution of the isotropic and homogeneous metric. If we suppose that there is some desert in the particle spectrum just below the Planck mass, then the effect of conformal trace anomaly is dominating at the corresponding energies. With some additional constraints on the particle content of the underlying gauge model (which favor extended or supersymmetric versions of the Standard Model rather than the minimal one), one arrives at the stable inflation. We review the model and report about the calculation of the gravitational waves on the background of the anomaly-induced inflation. The result for the perturbation spectrum is close to the one for the conventional inflaton model, and is in agreement with the existing Cobe data (see also [hep-th/0009197]).Comment: 4 pages, LaTeX. Contribution to the Proceedings of the EuroConference on Frontiers in Particle Astrophysics and Cosmology, 30 September - 5 October 2000. San Feliu, Spai

Adiabatic Invariants and Scalar Fields in a de Sitter Space-Time

The method of adiabatic invariants for time dependent Hamiltonians is applied to a massive scalar field in a de Sitter space-time. The scalar field ground state, its Fock space and coherent states are constructed and related to the particle states. Diverse quantities of physical interest are illustrated, such as particle creation and the way a classical probability distribution emerges for the system at late times.Comment: 9 pages, Latex, no figure

The Modified Dynamics as a Vacuum Effect

Why does there appear in the modified dynamics (MOND) an acceleration constant, a0, of cosmological significance? An intriguing possibility is that MOND, indeed inertia itself--as embodied in the actions of free particles and fields, is due to effects of the vacuum. Either cosmology enters local dynamics by affecting the vacuum, and inertia in turn, through a0; or, the same vacuum effect enters both MOND (through a0) and cosmology (e.g. through a cosmological constant). For the vacuum to serve as substratum for inertia a body must be able to read in it its non-inertial motion; this indeed it can, by detecting Unruh-type radiation. A manifestation of the vacuum is also seen, even by inertial observers, in a non-trivial universe (marked, e.g., by curvature or expansion). A non-inertial observer in a nontrivial universe will see the combined effect. An observer on a constant-acceleration (a) trajectory in a de Sitter universe with cosmological constant L sees Unruh radiation of temperature T\propto [a^2+a0^2]^{1/2}, with a0=(\L/3)^{1/2}. The temperature excess over what an inertial observer sees, T(a)-T(0), turns out to depend on a in the same way that MOND inertia does. An actual inertia-from-vacuum mechanism is still a far cry off.Comment: 6 pages, Latex, version to be published in Physics Letters

The no-defect conjecture in cosmic crystallography

The topology of space is usually assumed simply connected, but could be multi-connected. We review in the latter case the possibility that topological defects arising at high energy phase transitions might still be present and find that either they are very unlikely to form at all, or space is effectively simply connected on scales up to the horizon size.Comment: LaTeX-REVTeX, 5 pages and 2 figures uuencoded, submitted to Phys. Rev. Let

Space--time fluctuations and the spreading of wavepackets

Using a density matrix description in space we study the evolution of wavepackets in a fluctuating space-time background. We assume that space-time fluctuations manifest as classical fluctuations of the metric. From the non-relativistic limit of a non-minimally coupled Klein-Gordon equation we derive a Schr\"odinger equation with an additive gaussian random potential. This is transformed into an effective master equation for the density matrix. The solutions of this master equation allow to study the dynamics of wavepackets in a fluctuating space-time, depending on the fluctuation scenario. We show how different scenarios alter the diffusion properties of wavepackets.Comment: 11 page

Constraining interacting dark energy models with flux destabilization

A destabilization in the transfer energy flux from the vacuum to radiation, for two vacuum decay laws relevant to the dark energy problem, is analyzed using the Landau-Lifshitz fluctuation hydrodynamic theory. Assuming thermal (or near thermal) equilibrium between the vacuum and radiation, at the earliest epoch of the Universe expansion, we show that the law due to renormalization-group running of the cosmological constant term, with parameters chosen not to spoil the primordial nucleosynthesis scenario, does soon drive the flux to fluctuate beyond its statistical average value thereby distorting the cosmic background radiation spectrum beyond observational limits. While the law coming from the saturated holographic dark energy does not lead the flux to wildly fluctuate, a more realistic non--saturated form shows again such anomalous behavior.Comment: 12 pages, minor correction, to appear in Physics Letters

Experimental observation of the Bogoliubov transformation for a Bose-Einstein condensed gas

Phonons with wavevector $q/\hbar$ were optically imprinted into a Bose-Einstein condensate. Their momentum distribution was analyzed using Bragg spectroscopy with a high momentum transfer. The wavefunction of the phonons was shown to be a superposition of +q and -q free particle momentum states, in agreement with the Bogoliubov quasiparticle picture.Comment: 4 pages, 3 figures, please take postscript version for the best version of Fig

A Theory for the Conformal Factor in Quantum R2R^2 Gravity

A new theory for the conformal factor in R$^2$-gravity is developed. The infrared phase of this theory, which follows from the one-loop renormalization group equations for the whole quantum R$^2$-gravity theory is described. The one-loop effective potential for the conformal factor is found explicitly and a mechanism for inducing Einstein gravity at the minimum of the effective potential for the conformal factor is suggested. A comparison with the effective theory of the conformal factor induced by the conformal anomaly, and also aiming to describe quantum gravity at large distances, is done.Comment: 10 pages, LaTeX file, June 1-199