Hiding dark energy transitions at low redshift

We show that it is both observationally allowable and theoretically possible to have large fluctuations in the dark energy equation of state as long as they occur at ultra-low redshifts z<0.02. These fluctuations would masquerade as a local transition in the Hubble rate of a few percent or less and escape even future, high precision, high redshift measurements of the expansion history and structure. Scalar field models that exhibit this behavior have a sharp feature in the potential that the field traverses within a fraction of an e-fold of the present. The equation of state parameter can become arbitrarily large if a sharp dip or bump in the potential causes the kinetic and potential energy of the field to both be large and have opposite sign. While canonical scalar field models can decrease the expansion rate at low redshift, increasing the local expansion rate requires a non-canonical kinetic term for the scalar field.Comment: 4 pages, 2 figures; submitted to Phys. Rev. D (Brief Report

Evidence for horizon-scale power from CMB polarization

The CMB temperature power spectrum offers ambiguous evidence for the existence of horizon-scale power in the primordial power spectrum due to uncertainties in spatial curvature and the physics of cosmic acceleration as well as the observed low quadrupole. Current polarization data from WMAP provide evidence for horizon-scale power that is robust to these uncertainties. Polarization on the largest scales arises mainly from scattering at z<6 when the universe is fully ionized, making the evidence robust to ionization history variations at higher redshifts as well. A cutoff in the power spectrum is limited to C=k_C/10^{-4} Mpc^{-1}<5.2 (95% CL) by polarization, only slightly weaker than joint temperature and polarization constraints in flat LCDM (C<4.2). Planck should improve the polarization limit to C<3.6 for any model of the acceleration epoch and ionization history as well as provide tests for foreground and systematic contamination.Comment: 4 pages, 2 figures; submitted to Phys. Rev. D (Rapid Communications). Code for modified reionization in CAMB and CosmoMC available at http://background.uchicago.edu/camb_rpc

"Input-output Structure and Growth in China"

The fast and steady economic growth in China during the 1990s has attracted much international attention. Using the three most recent Chinese input-output tables, this paper investigates industry structure and inter-industry relationships and the relationship of both to economic growth. The input-output tables contain intermediate demand and final demand for six broad industries, namely, Agriculture, Industry, Construction, Transportation, Post and Telecommunications, Services, and Other, for 1992, 1995 and 1997, which enables computing of input-output coefficients for three time periods. As direct and indirect input-output coefficients characterise industry structure during a particular time period, changes over time reflect the patterns in industry structure evolvement. Furthermore, output growth in a particular industry can be analysed from two different sources, namely the changes in input-output coefficients that reflect technological change, and the change in final demand. This paper sheds light on four different issues over the five-year period from 1992 to 1997: (1) Was growth driven by technological changes or final demand increases? (2) As a result of the interdependence of industries, how did an increase in final demand in one industry affect growth in another? (3) How has the bottleneck of an insufficient capability in the Transportation, Post and Telecommunications sector to cope with demands from other sectors been affected during this period? (4) Has the industry structure of the economy been shifting in conformity with traditional growth theory, namely with a decline in the agricultural sector and a rise in the modern industrial sector?

Large deviations and averaging for systems of slow–fast reaction–diffusion equations

We study a large deviation principle for a system of stochastic reaction--diffusion equations (SRDEs) with a separation of fast and slow components and small noise in the slow component. The derivation of the large deviation principle is based on the weak convergence method in infinite dimensions, which results in studying averaging for controlled SRDEs. By appropriate choice of the parameters, the fast process and the associated control that arises from the weak convergence method decouple from each other. We show that in this decoupling case one can use the weak convergence method to characterize the limiting process via a "viable pair" that captures the limiting controlled dynamics and the effective invariant measure simultaneously. The characterization of the limit of the controlled slow-fast processes in terms of viable pair enables us to obtain a variational representation of the large deviation action functional. Due to the infinite--dimensional nature of our set--up, the proof of tightness as well as the analysis of the limit process and in particular the proof of the large deviations lower bound is considerably more delicate here than in the finite--dimensional situation. Smoothness properties of optimal controls in infinite dimensions (a necessary step for the large deviations lower bound) need to be established. We emphasize that many issues that are present in the infinite dimensional case, are completely absent in finite dimensions.First author draf

Large deviations and averaging for systems of slow--fast stochastic reaction--diffusion equations

We study a large deviation principle for a system of stochastic reaction--diffusion equations (SRDEs) with a separation of fast and slow components and small noise in the slow component. The derivation of the large deviation principle is based on the weak convergence method in infinite dimensions, which results in studying averaging for controlled SRDEs. By appropriate choice of the parameters, the fast process and the associated control that arises from the weak convergence method decouple from each other. We show that in this decoupling case one can use the weak convergence method to characterize the limiting process via a "viable pair" that captures the limiting controlled dynamics and the effective invariant measure simultaneously. The characterization of the limit of the controlled slow-fast processes in terms of viable pair enables us to obtain a variational representation of the large deviation action functional. Due to the infinite--dimensional nature of our set--up, the proof of tightness as well as the analysis of the limit process and in particular the proof of the large deviations lower bound is considerably more delicate here than in the finite--dimensional situation. Smoothness properties of optimal controls in infinite dimensions (a necessary step for the large deviations lower bound) need to be established. We emphasize that many issues that are present in the infinite dimensional case, are completely absent in finite dimensions

Introduction to the Bethe Ansatz III

Having introduced the magnon in part I and the spinon in part II as the relevant quasi-particles for the interpretation of the spectrum of low-lying excitations in the one-dimensional (1D) s=1/2 Heisenberg ferromagnet and antiferromagnet, respectively, we now study the low-lying excitations of the Heisenberg antiferromagnet in a magnetic field and interpret these collective states as composites of quasi-particles from a different species. We employ the Bethe ansatz to calculate matrix elements and show how the results of such a calculation can be used to predict lineshapes for neutron scattering experiments on quasi-1D antiferromagnetic compounds. The paper is designed as a tutorial for beginning graduate students. It includes 11 problems for further study.Comment: 11 page

Figures of merit for present and future dark energy probes

We compare current and forecasted constraints on dynamical dark energy models from Type Ia supernovae and the cosmic microwave background using figures of merit based on the volume of the allowed dark energy parameter space. For a two-parameter dark energy equation of state that varies linearly with the scale factor, and assuming a flat universe, the area of the error ellipse can be reduced by a factor of ~10 relative to current constraints by future space-based supernova data and CMB measurements from the Planck satellite. If the dark energy equation of state is described by a more general basis of principal components, the expected improvement in volume-based figures of merit is much greater. While the forecasted precision for any single parameter is only a factor of 2-5 smaller than current uncertainties, the constraints on dark energy models bounded by -1<w<1 improve for approximately 6 independent dark energy parameters resulting in a reduction of the total allowed volume of principal component parameter space by a factor of ~100. Typical quintessence models can be adequately described by just 2-3 of these parameters even given the precision of future data, leading to a more modest but still significant improvement. In addition to advances in supernova and CMB data, percent-level measurement of absolute distance and/or the expansion rate is required to ensure that dark energy constraints remain robust to variations in spatial curvature.Comment: 9 pages, 7 figures; submitted to Phys. Rev.