Numerical Study of a Two-Dimensional Quantum Antiferromagnet with Random Ferromagnetic Bonds

A Monte Carlo method for finite-temperature studies of the two-dimensional quantum Heisenberg antiferromagnet with random ferromagnetic bonds is presented. The scheme is based on an approximation which allows for an analytic summation over the realizations of the randomness, thereby significantly alleviating the ``sign problem'' for this frustrated spin system. The approximation is shown to be very accurate for ferromagnetic bond concentrations of up to ten percent. The effects of a low concentration of ferromagnetic bonds on the antiferromagnetism are discussed.Comment: 11 pages + 5 postscript figures (included), Revtex 3.0, UCSBTH-94-2

Models of quintessence coupled to the electromagnetic field and the cosmological evolution of alpha

We study the change of the effective fine structure constant in the cosmological models of a scalar field with a non-vanishing coupling to the electromagnetic field. Combining cosmological data and terrestrial observations we place empirical constraints on the size of the possible coupling and explore a large class of models that exhibit tracking behavior. The change of the fine structure constant implied by the quasar absorption spectra together with the requirement of tracking behavior impose a lower bound of the size of this coupling. Furthermore, the transition to the quintessence regime implies a narrow window for this coupling around $10^{-5}$ in units of the inverse Planck mass. We also propose a non-minimal coupling between electromagnetism and quintessence which has the effect of leading only to changes of alpha determined from atomic physics phenomena, but leaving no observable consequences through nuclear physics effects. In doing so we are able to reconcile the claimed cosmological evidence for a changing fine structure constant with the tight constraints emerging from the Oklo natural nuclear reactor.Comment: 13 pages, 10 figures, RevTex, new references adde

Fine-structure constant variability, equivalence principle and cosmology

It has been widely believed that variability of the fine-structure constant alpha would imply detectable violations of the weak equivalence principle. This belief is not justified in general. It is put to rest here in the context of the general framework for alpha variability [J. D. Bekenstein, Phys. Rev. D 25, 1527 (1982)] in which the exponent of a scalar field plays the role of the permittivity and inverse permeability of the vacuum. The coupling of particles to the scalar field is necessarily such that the anomalous force acting on a charged particle by virtue of its mass's dependence on the scalar field is cancelled by terms modifying the usual Coulomb force. As a consequence a particle's acceleration in external fields depends only on its charge to mass ratio, in accordance with the principle. And the center of mass acceleration of a composite object can be proved to be independent of the object's internal constitution, as the weak equivalence principle requires. Likewise the widely employed assumption that the Coulomb energy of matter is the principal source of the scalar field proves wrong; Coulomb energy effectively cancels out in the continuum description of the scalar field's dynamics. This cancellation resolves a cosmological conundrum: with Coulomb energy as source of the scalar field, the framework would predict a decrease of alpha with cosmological expansion, whereas an increase is claimed to be observed. Because of the said cancellation, magnetic energy of cosmological baryonic matter is the main source of the scalar field. Consequently the expansion is accompanied by an increase in alpha; for reasonable values of the framework's sole parameter, this occurs at a rate consistent with the observers' claims.Comment: RevTeX-4, 22 pages, no figures, added a section on caveats as well as several new references with discussion of them in body. To appear in Phys. Rev.

Role of Modified Chaplygin Gas as a Dark Energy Model in Collapsing Spherically Symmetric Cloud

In this work, gravitational collapse of a spherical cloud, consists of both dark matter and dark energy in the form of modified Chaplygin gas is studied. It is found that dark energy alone in the form of modified Chaplygin gas forms black hole. Also when both components of the fluid are present then the collapse favors the formation of black hole in cases the dark energy dominates over dark matter. The conclusion is totally opposite to the usually known results.Comment: 7 Latex Pages, RexTex style, No figure

Interacting Modified Variable Chaplygin Gas in Non-flat Universe

A unified model of dark energy and matter is presented using the modified variable Chaplygin gas for interacting dark energy in a non-flat universe. The two entities interact with each other non-gravitationally which involves a coupling constant. Due to dynamic interaction, the variation in this constant arises that henceforth changes the equations of state of these quantities. We have derived the effective equations of state corresponding to matter and dark energy in this interacting model. Moreover, the case of phantom energy is deduced by putting constraints on the parameters involved.Comment: 9 pages; Accepted for publication in European Physical Journal

Quintessence and variation of the fine structure constant in the CMBR

We study dependence of the CMB temperature anisotropy spectrum on the value of the fine structure constant $\alpha$ and the equation of state of the dark energy component of the total density of the universe. We find that bounds imposed on the variation of $\alpha$ from the analysis of currently available CMB data sets can be significantly relaxed if one also allows for a change in the equation of state.Comment: 5 pages, 3 figures. Several references added and a few minor typos corrected in the revised versio

Measuring α\alpha in the Early Universe: CMB Temperature, Large-Scale Structure and Fisher Matrix Analysis

We extend our recent work on the effects of a time-varying fine-structure constant $\alpha$ in the cosmic microwave background, by providing a thorough analysis of the degeneracies between $\alpha$ and the other cosmological parameters, and discussing ways to break these with both existing and/or forthcoming data. In particular, we present the state-of-the-art CMB constraints on $\alpha$, through a combined analysis of the BOOMERanG, MAXIMA and DASI datasets. We also present a novel discussion of the constraints on $\alpha$ coming from large-scale structure observations, focusing in particular on the power spectrum from the 2dF survey. Our results are consistent with no variation in $\alpha$ from the epoch of recombination to the present day, and restrict any such (relative) variation to be less than about 4%. We show that the forthcoming MAP and (particularly) Planck experiments will be able to break most of the currently existing degeneracies between $\alpha$ and other parameters, and measure $\alpha$ to better than percent accuracy.Comment: 11 pages in RevTex4 format. Low-quality figures to comply with arXiv restrictions (better ones available from the authors). v2: Updated Oklo discussion, plus other cosmetic changes. Version to appear in Phys Rev

The Equivalence Principle and the Constants of Nature

We briefly review the various contexts within which one might address the issue of ``why'' the dimensionless constants of Nature have the particular values that they are observed to have. Both the general historical trend, in physics, of replacing a-priori-given, absolute structures by dynamical entities, and anthropic considerations, suggest that coupling ``constants'' have a dynamical nature. This hints at the existence of observable violations of the Equivalence Principle at some level, and motivates the need for improved tests of the Equivalence Principle.Comment: 12 pages; invited talk at the ISSI Workshop on the Nature of Gravity: Confronting Theory and Experiment in Space, Bern, Switzerland, 6-10 October 2008; to appear in Space Science Review

Constraints on coupling constant between dark energy and dark matter

We have investigated constraints on the coupling between dark matter and the interacting Chaplygin gas. Our results indicate that the coupling constant $c$ between these two entities can take arbitrary values, which can be either positive or negative, thus giving arbitrary freedom to the inter-conversion between Chaplygin gas and dark matter. Thus our results indicate that the restriction $0<c<1$ on the coupling constant occurs as a very special case. Our analysis also supports the existence of phantom energy under certain conditions on the coupling constant.Comment: 16 Pages, 3 figure

Cosmological Variation of the Fine Structure Constant from an Ultra-Light Scalar Field: The Effects of Mass

Cosmological variation of the fine structure constant $\alpha$ due to the evolution of a spatially homogeneous ultra-light scalar field ($m \sim H_0$) during the matter and $\Lambda$ dominated eras is analyzed. Agreement of $\Delta \alpha/\alpha$ with the value suggested by recent observations of quasar absorption lines is obtained by adjusting a single parameter, the coupling of the scalar field to matter. Asymptotically $\alpha(t)$ in this model goes to a constant value $\bar{\alpha} \approx \alpha_0$ in the early radiation and the late $\Lambda$ dominated eras. The coupling of the scalar field to (nonrelativistic) matter drives $\alpha$ slightly away from $\bar{\alpha}$ in the epochs when the density of matter is important. Simultaneous agreement with the more restrictive bounds on the variation $|\Delta \alpha/\alpha|$ from the Oklo natural fission reactor and from meteorite samples can be achieved if the mass of the scalar field is on the order of 0.5--0.6 $H_\Lambda$, where $H_\Lambda = \Omega_\Lambda^{1/2} H_0$. Depending on the scalar field mass, $\alpha$ may be slightly smaller or larger than $\alpha_0$ at the times of big bang nucleosynthesis, the emission of the cosmic microwave background, the formation of early solar system meteorites, and the Oklo reactor. The effects on the evolution of $\alpha$ due to nonzero mass for the scalar field are emphasized. An order of magnitude improvement in the laboratory technique could lead to a detection of $(\dot{\alpha}/\alpha)_0$.Comment: 22 pages, 15 figures Version 2: The Oklo event is now considered as localized in time. The initial conditions for the scalar field have been refined. The numbers in the Table have been recomputed. Added Ref