Superstring cosmology: Is it consistent with a matter-dominated universe?

It is shown that if our universe is described by the cosmological, classical, Einstein equations based on a manifold M⁴ × G where G is the product of any number of Ricci flat manifolds (as is expected to occur in superstring theories) then our universe must, today, be radiation dominated. A matter-dominated universe (or an inflationary universe) would lead to large variations in the size of the extra dimensions. This would lead to changes in coupling constants of sufficiently large magnitude to be rules out by observation. If a model based on M⁴ x G with G Ricci flat is to viable, there are only two possibilities. Either the universe is radiation dominated today (for which no satisfactory model exists) or the compactification is controlled dominantly by some (thus far) unquantifiable “quantum gravity” effects.     

Does a randall-sundrum scenario create the illusion of a torsion-free universe?

We consider spacetime with torsion in a Randall-Sundrum scenario where torsion, identified with the rank-2 Kalb-Ramond field, exists in the bulk together with gravity. While the interactions of both graviton and torsion in the bulk are controlled by the Planck mass, an additional exponential suppression comes for the torsion zero-mode on the visible brane. This may serve as a natural explanation of why the effect of torsion is so much weaker than that of curvature on the brane. The massive torsion modes, on the other hand, are correlated with the corresponding gravitonic modes and may be detectable in TeV-scale experiments.     

On stable variants of Einstein’s static universe

The investigation of the stability properties of certain variants of Einstein’s static universe performed by Carneiro and Tavakol (in Stability of the Einstein static universe in the presence of vacuum energy) is generalized. It is shown that all versions of Einstein’s static universe without interaction between the two fluids it contains are unstable. Interaction between the fluids may stabilize the universe. The condition for stability by perturbation of the scale factor from its static value is deduced for a class of universe models containing those investigated by Carneiro and Tavakol. Stability of the static state requires that energy is transformed to matter during such a perturbation.     

Searching for a response: the intriguing mystery of Feynman’s theoretical reference amplifier

We analyze Feynman’s work on the response of an amplifier performed at Los Alamos and described in a technical report of 1946, as well as lectured on at the Cornell University in 1946–47 during his course on Mathematical Methods. The motivation for such a work was Feynman’s involvement in the Manhattan Project, for which the necessity emerged of feeding the output pulses of counters into amplifiers or several other circuits, with the risk of introducing distortion at each step. In order to deal with such a problem, Feynman designed a theoretical “reference amplifier”, thus enabling a characterization of the distortion by means of a benchmark relationship between phase and amplification for each frequency, and providing a standard tool for comparing the operation of real devices. A general theory was elaborated, from which he was able to deduce the basic features of an amplifier just from its response to a pulse or to a sine wave of definite frequency. Moreover, in order to apply such a theory to practical problems, a couple of remarkable examples were worked out, both for high-frequency cutoff amplifiers and for low-frequency ones. A special consideration deserves a mysteriously exceptional amplifier with best stability behavior introduced by Feynman, for which different physical interpretations are here envisaged. Feynman’s earlier work then later flowed in the Hughes lectures on Mathematical Methods in Physics and Engineering of 1970–71, where he also remarked on causality properties of an amplifier, that is on certain relations between frequency and phase shift that a real amplifier has to satisfy in order not to allow output signals to appear before input ones. Quite interestingly, dispersion relations to be satisfied by the response function were introduced.

     

Supersymmetric quantum cosmology: a ‘Socratic’ guide

We calculate the classical limit effective action of the EPRL/FK spinfoam model of quantum gravity coupled to matter fields. By employing the standard QFT background field method adapted to the spinfoam setting, we find that the model has many different classical effective actions. Most notably, these include the ordinary Einstein–Hilbert action coupled to matter, but also an action which describes antigravity. All those multiple classical limits appear as a consequence of the fact that the EPRL/FK vertex amplitude has cosine-like large spin asymptotics. We discuss some possible ways to eliminate the unwanted classical limits.     

Can the CMB reveal the topology of the universe?

This article summarizes recent progress in the development of tools to study the topology of the universe with the cosmic microwave background. The different signatures of the topology and observational constraints are described. The ability of future experiments to reveal the topological structure of our universe is then discussed. To cite this article: J.P. Uzan, A. Riazuelo, C. R. Physique 4 (2003).     

On the Violation of Ohm’s Law for Bounded Interactions: a One Dimensional System

We consider an infinite Hamiltonian system in one space dimension, given by a charged particle subjected to a constant electric field and interacting with an infinitely extended system of particles. We discuss conditions on the particle/medium interaction which are necessary for the charged particle to reach a finite limiting velocity. We assume that the background system is initially in an equilibrium Gibbs state and we prove that for bounded interactions the average velocity of the charged particle increases linearly in time. This statement holds for any positive intensity of the electric field, thus contradicting Ohms law.Work partially supported by the GNFM-INDAM and the Italian Ministry of the University.     

Are Kaluza-Klein models of the universe chaotic?

The generic behavior of vacuum inhomogeneous and spatially homogeneous Kaluza-Klein models is studied in the vicinity of the cosmological singularity. It is shown that, in space-time dimensions 11, the generalized Kasner solution, with monotonic power-law behavior of the spatial distances, becomes a general solution of the Einstein vacuum field equations and that, moreover, the chaotic oscillatory behavior disappears.On the other hand, the chaotic oscillatory behavior, absent in diagonal spatially homogeneous cosmological models in space-time dimensions between 5 and 10, can be reestablished when off-diagonal terms are included.     

A study of non-extensivity in the Earth’s magnetosphere

Magnetic storms are undoubtedly among the most important phenomena in space physics and also a central subject of space weather. The non-extensive Tsallis entropy has been recently introduced, as an effective complexity measure for the analysis of the geomagnetic activity D _st index. Tsallis entropy has been shown to sensitively detect the complexity dissimilarity between pre-storm activity and intense magnetic storms in the Earth’s magnetosphere. Here, we show that the D _st time series obey a modified form of the Gutenberg-Richter law for the case of non-extensive statistics, thus providing evidence for universality in magnetic storm and earthquake occurrence.     

Comparative study of the specific heat of superconducting and non-superconducting YBa2Cu3O7−x

We have measured the specific heat, the electrical resistance and the magnetic susceptibility of YBa₂Cu₃O_7–x in a superconducting (sc) and in a non-superconducting (nsc) version. The latter was obtained by inducing a small loss of oxygen. In the sc sample we find a jump of the specific heat with C=3.6 J mole^–1 K^–1. Below the maximum nearT _c the specific heat of the sc version drops too fast for an electronic effect alone: there is a cross-over from excess to deficiency already at 0.9T _c . The specific heat of the nsc version shows a change of slope in the temperature range between 70 and 80 K, which indicates the existence of a second specific heat anomaly, which apparently exists independently of that due to the onset of superconductivity and explains at least partially the premature crossover.Alexander von Humboldt fellow. On leave in absence from Centro Atomico Bariloche—CNEA Argentina     

Can the universe fragment into many independent causal patches at turnaround in cyclic cosmology?

Infinitely cyclic cosmology is often frustrated by the second law of thermodynamics which dictates that the entropy increases from cycle to cycle so that extrapolation into the past will lead back to an initial singularity. It has been argued in the literature that the entropy problem can be resolved in a particular cyclic universe model through a deflation mechanism (i.e., the universe fragments into an astronomically large number of disconnected causal patches at the turnaround). We point out that in this cyclic model the Hubble distance will become infinity at the turnaround; thus the deflation scenario does not seem to be valid.     

Is thermodynamics of the universe bounded by event horizon a Bekenstein system?

In this brief communication, we have studied the validity of the first law of thermodynamics for the universe bounded by event horizon with two examples. The key point is the appropriate choice of the temperature on the event horizon. Finally, we have concluded that universe bounded by the event horizon may be a Bekenstein system and Einstein?s equations and the first law of thermodynamics on the event horizons are equivalent.     

New Analytical Solution of the Equilibrium Ampere’s Law Using the Walker’s Method: a Didactic Example

This work aims to demonstrate the analytical solution of the Grad-Shafranov (GS) equation or generalized Ampere’s law, which is important in the studies of self-consistent 2.5-D solution for current sheet structures. A detailed mathematical development is presented to obtain the generating function as shown by Walker (RSPSA 91, 410, 1915). Therefore, we study the general solution of the GS equation in terms of the Walker’s generating function in details without omitting any step. The Walker’s generating function g(ζ) is written in a new way as the tangent of an unspecified function K(ζ). In this trend, the general solution of the GS equation is expressed as exp(??2Ψ) =?4|K ^′(ζ)|²/cos²[K(ζ) ? K(ζ ^?)]. In order to investigate whether our proposal would simplify the mathematical effort to find new generating functions, we use Harris’s solution as a test, in this case K(ζ) = arctan(exp(i ζ)). In summary, one of the article purposes is to present a review of the Harris’s solution. In an attempt to find a simplified solution, we propose a new way to write the GS solution using g(ζ) = tan(K(ζ)). We also present a new analytical solution to the equilibrium Ampere’s law using g(ζ) = cosh(b ζ), which includes a generalization of the Harris model and presents isolated magnetic islands.     

Initial conditions of the universe: how much isocurvature is allowed?

We investigate the constraints imposed by current data on correlated mixtures of adiabatic and nonadiabatic primordial perturbations. We discover subtle flat directions in parameter space that tolerate large (approximately 60%) fractions of nonadiabatic fluctuations. In particular, larger values of the baryon density and a spectral tilt are allowed. The cancellations in the degenerate directions are explored and the role of priors is elucidated.     

Feynman’s Proof of Maxwell Equations: in?the?Context?of Quantum Gravity

Many of us are familiar with Feynman’s “proof” of 1948, as revealed by Dyson, which demonstrates that Maxwell equations of electromagnetism are a consequence of Newton’s laws of motion of classical mechanics and the commutation relations of coordinate and momentum of quantum mechanics. It was Feynman’s purpose to explore the universality of dynamics of particles while making the fewest assumptions. We re-examine this formulation in the context of quantum gravity and show how Feynman’s derivation can be extended to include quantum gravity.     

Alternative Proof for the Localization of Sinai’s Walk

We give an alternative proof of the localization of Sinais random walk in random environment under weaker hypothesis than the ones used by Sinai. Moreover, we give estimates that are stronger than the one of Sinai on the localization neighborhood and on the probability for the random walk to stay inside this neighborhood.