arXiv subjects

Greg Huey

Publications and source records attributed to Greg Huey.

17 recordsLinked to original sources

arXiv2026

Obstructions to Deformation Quantization of Bundles

Let $\left(M, \mathcal{O}_M \right)$ be a smooth algebraic variety over field $\kappa$ of characteristic $0$ with an algebraic symplectic form $\omega$, or a complex manifold with a holomorphic form $\omega$. Furthermore, let $E$ be a vector bundle over $\left(M, \mathcal{O}_M \right)$ and $\mathcal{O}_{\hbar}$ a deformation quantization of $\mathcal{O}_M$ compatible with $\omega$. Assuming that $E$ possesses a deformation quantization to order $\hbar^k$ we consider the problem of extending it to order $\hbar^\ell$ for $\ell > k$, and establish triviality of an obstruction class as a necessary condition for this extension to exist. Furthermore, in the case $\ell \le 2k+1$, we prove that this condition is also sufficient.

math.AG↗

arXiv2023

Membrane Models as a Means of Propulsion in General Relativity: Super-Luminal Warp-Drive that Satisfies the Weak Energy Condition

Presented are toy-models for sub-luminal and super-luminal warp-drives in 3+1 dimensions. The models are constructed in a chimeric manner - as different bulk space-times separated by thin membranes. The membranes contain perfect-fluid-like stress-energy tensors. The Israel junction conditions relate this stress-energy to a jump in extrinsic curvature across the brane, which in turn manifests as apparent acceleration in the bulk space-times. The acceleration on either side of the brane may be set individually by choice of model parameters. The Weak Energy Condition (WEC) is shown to be satisfied everywhere in both models. Although the branes in these toy models are not compact, it is demonstrated that super-luminal warp-drive is possible that satisfies the WEC. Additionally, the nature of these models provides framework for speculation on a mechanism for transition from sub-luminal to super-luminal warp. Neither quantum effects nor stability of the models is considered.

gr-qc↗

arXiv2021

Symmetry-Breaking in Plant Stems

The purpose of this paper is to present a model of a phenomenon of plant stem morphogenesis observed by Cesar Gomez-Campo in 1970. We consider a simplified model of auxin dynamics in plant stems, showing that, after creation of the original primordium, it can represent random, distichous and spiral phyllotaxis (leaf arrangement) just by varying one parameter, the rate of diffusion. The same analysis extends to the $n$-jugate case where $n$ primordia are initiated at each plastochrone. Having validated the model, we consider how it can give rise to the Gomez-Campo phenomenon, showing how a stem with spiral phyllotaxis can produce branches of the same or opposite chirality. And finally, how the relationship can change from discordant to concordant over the course of a growing season.

q-bio.QM↗

arXiv2008

CMB likelihood approximation by a Gaussianized Blackwell-Rao estimator

We introduce a new CMB temperature likelihood approximation called the Gaussianized Blackwell-Rao (GBR) estimator. This estimator is derived by transforming the observed marginal power spectrum distributions obtained by the CMB Gibbs sampler into standard univariate Gaussians, and then approximate their joint transformed distribution by a multivariate Gaussian. The method is exact for full-sky coverage and uniform noise, and an excellent approximation for sky cuts and scanning patterns relevant for modern satellite experiments such as WMAP and Planck. A single evaluation of this estimator between l=2 and 200 takes ~0.2 CPU milliseconds, while for comparison, a single pixel space likelihood evaluation between l=2 and 30 for a map with ~2500 pixels requires ~20 seconds. We apply this tool to the 5-year WMAP temperature data, and re-estimate the angular temperature power spectrum, $C_{\ell}$, and likelihood, L(C_l), for l<=200, and derive new cosmological parameters for the standard six-parameter LambdaCDM model. Our spectrum is in excellent agreement with the official WMAP spectrum, but we find slight differences in the derived cosmological parameters. Most importantly, the spectral index of scalar perturbations is n_s=0.973 +/- 0.014, 1.9 sigma away from unity and 0.6 sigma higher than the official WMAP result, n_s = 0.965 +/- 0.014. This suggests that an exact likelihood treatment is required to higher l's than previously believed, reinforcing and extending our conclusions from the 3-year WMAP analysis. In that case, we found that the sub-optimal likelihood approximation adopted between l=12 and 30 by the WMAP team biased n_s low by 0.4 sigma, while here we find that the same approximation between l=30 and 200 introduces a bias of 0.6 sigma in n_s.

astro-ph↗

arXiv2007

Bayesian analysis of the low-resolution polarized 3-year WMAP sky maps

We apply a previously developed Gibbs sampling framework to the foreground corrected 3-yr WMAP polarization data and compute the power spectrum and residual foreground template amplitude posterior distributions. We first analyze the co-added Q- and V-band data, and compare our results to the likelihood code published by the WMAP team. We find good agreement, and thus verify the numerics and data processing steps of both approaches. However, we also analyze the Q- and V-bands separately, allowing for non-zero EB cross-correlations and including two individual foreground template amplitudes tracing synchrotron and dust emission. In these analyses, we find tentative evidence of systematics: The foreground tracers correlate with each of the Q- and V-band sky maps individually, although not with the co-added QV map; there is a noticeable negative EB cross-correlation at l <~ 16 in the V-band map; and finally, when relaxing the constraints on EB and BB, noticeable differences are observed between the marginalized band powers in the Q- and V-bands. Further studies of these features are imperative, given the importance of the low-l EE spectrum on the optical depth of reionization tau and the spectral index of scalar perturbations n_s.

astro-ph↗

arXiv2006

Estimation of Polarized Power Spectra by Gibbs sampling

Earlier papers introduced a method of accurately estimating the angular cosmic microwave background (CMB) temperature power spectrum based on Gibbs sampling. Here we extend this framework to polarized data. All advantages of the Gibbs sampler still apply, and exact analysis of mega-pixel polarized data sets is thus feasible. These advantages may be even more important for polarization measurements than for temperature measurements. While approximate methods can alias power from the larger E-mode spectrum into the weaker B-mode spectrum, the Gibbs sampler (or equivalently, exact likelihood evaluations) allows for a statistically optimal separation of these modes in terms of power spectra. To demonstrate the method, we analyze two simulated data sets: 1) a hypothetical future CMBPol mission, with the focus on B-mode estimation; and 2) a Planck-like mission, to highlight the computational feasibility of the method.

astro-ph↗

arXiv2006

A re-analysis of the three-year WMAP temperature power spectrum and likelihood

We analyze the three-year WMAP temperature anisotropy data seeking to confirm the power spectrum and likelihoods published by the WMAP team. We apply five independent implementations of four algorithms to the power spectrum estimation and two implementations to the parameter estimation. Our single most important result is that we broadly confirm the WMAP power spectrum and analysis. Still, we do find two small but potentially important discrepancies: On large angular scales there is a small power excess in the WMAP spectrum (5-10% at l<~30) primarily due to likelihood approximation issues between 13 <= l <~30. On small angular scales there is a systematic difference between the V- and W-band spectra (few percent at l>~300). Recently, the latter discrepancy was explained by Huffenberger et al. (2006) in terms of over-subtraction of unresolved point sources. As far as the low-l bias is concerned, most parameters are affected by a few tenths of a sigma. The most important effect is seen in n_s. For the combination of WMAP, Acbar and BOOMERanG, the significance of n_s =/ 1 drops from ~2.7 sigma to ~2.3 sigma when correcting for this bias. We propose a few simple improvements to the low-l WMAP likelihood code, and introduce two important extensions to the Gibbs sampling method that allows for proper sampling of the low signal-to-noise regime. Finally, we make the products from the Gibbs sampling analysis publically available, thereby providing a fast and simple route to the exact likelihood without the need of expensive matrix inversions.

astro-ph↗

arXiv2005

A Comprehensive Approach to Resolving the Nature of the Dark Energy

A data-driven approach to elucidating the nature of the dark energy, in the form of a joint analysis of a full set of cosmological parameters, utilizing all available observational data is proposed. A parameterization of a generalized dark energy is developed with the extension of fluid perturbation theory to models which cross through an equation of state of -1. This parameterization is selected to be general enough to admit a wide variety of behavior, while still being physical and economical. A Fisher matrix analysis with future high-precision CMB, cluster survey, and SNIa data suggests the parameters will probably be resolvable in the foreseeable future. How accurately the parameters can be determined depends sensitively on the nature of the dark energy - particularly how significant of a fraction of the total energy density it has been in the past. Parameter space will be sampled at a large number of points, with cosmological information such as CMB, power spectra, etc of each point being archived. Thus the likelihood functions of an arbitrary set of experiments can be applied to parameter space with insignificant new computational cost, making a wide variety of analyses possible. The resulting tool for Analysis and Resolution of Dark-sector Attributes, ARDA, will be highly versatile and adaptable. ARDA will allow the scientific community to extract parameters with an arbitrary set of experiments and theoretical priors, test for tension between classes of observations and investigate the effectiveness of hypothetical experiments, while evolving in a data-driven manner. A proof-of-concept prototype web-tool, \underbar{The Cosmic Concordance Project}, is already available.

astro-ph↗

arXiv2004

Precision Primordial $^4$He Measurement with CMB Experiments

Big bang nucleosynthesis (BBN) and the cosmic microwave background (CMB) are two major pillars of cosmology. Standard BBN accurately predicts the primordial light element abundances ($^4$He, D, $^3$He and $^7$Li), depending on one parameter, the baryon density. Light element observations are used as a baryometers. The CMB anisotropies also contain information about the content of the universe which allows an important consistency check on the Big Bang model. In addition CMB observations now have sufficient accuracy to not only determine the total baryon density, but also resolve its principal constituents, H and $^4$He. We present a global analysis of all recent CMB data, with special emphasis on the concordance with BBN theory and light element observations. We find $Ω_{B}h^{2}=0.025+0.0019-0.0026$ and $Y_{p}=0.250+0.010-0.014$ (fraction of baryon mass as $^4$He) using CMB data alone, in agreement with $^4$He abundance observations. With this concordance established we show that the inclusion of BBN theory priors significantly reduces the volume of parameter space. In this case, we find $Ω_{B}h^2=0.0244+0.00137-0.00284$ and $Y_p = 0.2493+0.0006-0.001$. We also find that the inclusion of deuterium abundance observations reduces the $Y_p$ and $Ω_{B}h^2$ ranges by a factor of $\sim $2. Further light element observations and CMB anisotropy experiments will refine this concordance and sharpen BBN and the CMB as tools for precision cosmology.

astro-ph↗

arXiv2004

Interacting Quintessence, Cosmic Acceleration and the Coincidence Problem

Faced by recent evidence for a flat universe dominated by dark energy, cosmologists grapple with deep cosmic enigmas such as the cosmological constant problem, extreme fine-tuning and the cosmic coincidence problem. The extent to which we observe the dimming of distant supernovae suggests that the cosmic acceleration is as least as severe as in cosmological constant models. Extrapolating this to our cosmic future implies terrifying visions of either a cold and empty universe or an explosive demise in a ``Big Rip.'' We construct a class of dynamical scalar field models of dark energy and dark matter. Within this class we can explain why supernovae imply a cosmic equation of state $w\lesssim-1$, address fine tuning issues, protect the universe from premature acceleration and predict a constant fraction of dark energy to dark matter in the future (thus solving the coincidence problem), satisfy the dominant energy condition, and ensure that gravitationally bound objects remain so forever (avoid a Big Rip). This is achieved with a string theory inspired Lagrangian containing standard kinetic terms, exponential potentials and couplings, and parameters of order unity.

astro-ph↗

arXiv2002

Inflation and Braneworlds: Degeneracies and Consistencies

Scalar and tensor perturbations arising in an inflationary braneworld scenario driven by a single scalar field are considered, where the bulk on either side of the brane corresponds to Anti-de Sitter spaces with different cosmological constants. A consistency relation between the two spectra is derived and found to have an identical form to that arising in standard single-field inflation based on conventional Einstein gravity. The dS/CFT correspondence may provide further insight into the origin of this degeneracy. Possible ways of lifting such a degeneracy are discussed.

astro-ph↗

arXiv2001

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 $α$ 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 $α$ 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.

astro-ph↗

arXiv2001

Robustness of the Quintessence Scenario in Particle Cosmologies

We study the robustness of the quintessence tracking scenario in the context of more general cosmological models that derive from high-energy physics. We consider the effects of inclusion of multiple scalar fields, corrections to the Hubble expansion law (such as those that arise in brane cosmological models), and potentials that decay with expansion of the Universe. We find that in a successful tracking quintessence model the average equation of state must remain nearly constant. Overall, the conditions for successful tracking become more complex in these more general settings. Tracking can become more fragile in presence of multiple scalar fields, and more stable when temperature dependent potentials are present. Interestingly though, most of the cases where tracking is disrupted are those in which the cosmological model is itself non-viable due to other constraints. In this sense tracking remains robust in models that are cosmologically viable.

astro-ph↗

arXiv2001

Inflation, braneworlds and quintessence

Inflationary cosmology is developed in the second Randall-Sundrum braneworld scenario, where the accelerated expansion arises through potentials that are too steep to drive inflation in conventional cosmology. A relationship between the scalar and tensor perturbation spectra is derived that is independent of both the inflaton potential and the brane tension. It is found that a single field with an inverse power law potential can act as both the inflaton and the quintessence field for suitable values of the brane tension.

astro-ph↗

arXiv2000

A Cosmological Mechanism for Stabilizing Moduli

In this paper, we show how the generic coupling of moduli to the kinetic energy of ordinary matter fields results in a cosmological mechanism that influences the evolution and stability of moduli. As an example, we reconsider the problem of stabilizing the dilaton in a non-perturbative potential induced by gaugino condensates. A well-known difficulty is that the potential is so steep that the dilaton field tends to overrun the correct minimum and to evolve to an observationally unacceptable vacuum. We show that the dilaton coupling to the thermal energy of matter fields produces a natural mechanism for gently relaxing the dilaton field into the correct minimum of the potential without fine-tuning of initial conditions. The same mechanism is potentially relevant for stabilizing other moduli fields.

hep-th↗

arXiv1998

Resolving the Cosmological Missing Energy Problem

Some form of missing energy may account for the difference between the observed cosmic matter density and the critical density. Two leading candidates are a cosmological constant and quintessence (a time-varying, inhomogenous component with negative pressure). We show that an ideal, full-sky cosmic background anisotropy experiment may not be able to distinguish the two, even when non-linear effects due to gravitational lensing are included. Due to this ambiguity, microwave background experiments alone may not determine the matter density or Hubble constant very precisely. We further show that degeneracy may remain even after considering classical cosmological tests and measurements of large scale structure.

astro-ph↗

arXiv1997

Parametric Resonance in an Expanding Universe

Parametric resonance has been discussed as a mechanism for copious particle production following inflation. Here we present a simple and intuitive calculational method for estimating the efficiency of parametric amplification as a function of parameters. This is important for determining whether resonant amplification plays an important role in the reheating process. We find that significant amplification occurs only for a limited range of couplings and interactions.

astro-ph↗