arXiv subjects

Patrick McDonald

Publications and source records attributed to Patrick McDonald.

At least 91 records · Page 5Linked to original sources

arXiv2006

One-Loop Renormalization of Pure Yang-Mills with Lorentz Violation

The explicit one-loop renormalizability of pure Yang-Mills theory with Lorentz violation is demonstrated. The result is consistent with multiplicative renormalization as the required counter terms are consistent with a single re-scaling of the Lorentz-violation parameters. In addition, the resulting beta functions indicate that the CPT-even Lorentz-violating terms increase with energy scale in opposition to the asymptotically free gauge coupling and CPT-odd terms. The calculations are performed at lowest-order in the Lorentz-violating terms as they are assumed small.

hep-ph↗

arXiv2006

Dark energy and curvature from a future baryonic acoustic oscillation survey using the Lyman-alpha forest

We explore the requirements for a Lyman-alpha forest (LyaF) survey designed to measure the angular diameter distance and Hubble parameter at 2~ 250 spectrograph is sufficient to measure both the radial and transverse oscillation scales to 1.4% from the LyaF (or better, if fainter magnitudes and possibly Lyman-break galaxies can be used). At fixed integration time and in the sky-noise-dominated limit, a wider, noisier survey is generally more efficient; the only fundamental upper limit on noise being the need to identify a quasar and find a redshift. Because the LyaF is much closer to linear and generally better understood than galaxies, systematic errors are even less likely to be a problem.

astro-ph↗

arXiv2006

Can sterile neutrinos be the dark matter?

We use the Ly-alpha forest power spectrum measured by the SDSS and high-resolution spectroscopy observations in combination with cosmic microwave background and galaxy clustering constraints to place limits on a sterile neutrino as a dark matter candidate in the warm dark matter (WDM) scenario. Such a neutrino would be created in the early universe through mixing with an active neutrino and would suppress structure on scales smaller than its free streaming scale. We ran a series of high-resolution hydrodynamic simulations with varying neutrino mass to describe the effect of a sterile neutrino on the Ly-alpha forest power spectrum. We find that the mass limit is m_s >14 keV at 95% c.l. (10keV at 99.9%), which is nearly an order of magnitude tighter constraint than previously published limits and is above the upper limit allowed by X-ray constraints, excluding this candidate as dark matter in this model. The corresponding limit for a neutrino that decoupled early while in thermal equilibrium is 2.5keV (95% c.l.).

astro-ph↗

arXiv2006

Bose-Einstein Condensates as a Probe for Lorentz Violation

The effects of small Lorentz-violating terms on Bose-Einstein condensates are analyzed. We find that there are changes to the phase and shape of the ground-state wave function that vary with the orientation of the trap. In addition, spin-couplings can act as a source for spontaneous symmetry breaking in ferromagnetic condensates making them sensitive probes for fundamental symmetry violation.

hep-ph↗

arXiv2005

Dependence of the non-linear mass power spectrum on the equation of state of dark energy

We present N-body simulation calculations of the dependence of the power spectrum of non-linear cosmological mass density fluctuations on the equation of state of the dark energy, w=p/rho. At fixed linear theory power, increasing w leads to an increase in non-linear power, with the effect increasing with k. By k=10 h/Mpc, a model with w=-0.75 has ~12% more power than a standard cosmological constant model (w=-1), while a model with w=-0.5 has ~33% extra power (at z=0). The size of the effect increases with increasing dark energy fraction, and to a lesser extent increasing power spectrum normalization, but is insensitive to the power spectrum shape (the numbers above are for Omega_m=0.281 and sigma_8=0.897). A code quantifying the non-linear effect of varying w, as a function of k, z, and other cosmological parameters, which should be accurate to a few percent for k<10 h/Mpc for models that fit the current observations, is available at http://www.cita.utoronto.ca/~pmcdonal/code.html. This paper also serves as an example of a detailed exploration of the numerical convergence properties of ratios of power spectra for different models, which can be useful because some kinds of numerical error cancel in a ratio. When precision calculations based on numerical simulations are needed for many different models, efficiency may be gained by breaking the problem into a calculation of the absolute prediction at a central point, and calculations of the relative change in the prediction with model parameters.

astro-ph↗

arXiv2004

Nonrelativisitic Ideal Gasses and Lorentz Violations

We develop statistical mechanics for a nonrelativisitic ideal gas in the presence of Lorentz violating background fields. The analysis is performed using the Standard-Model Extension (SME). We derive the corresponding laws of thermodynamics and find that, to lowest order in Lorentz violation, the scalar thermodynamic variables are corrected by a rotationally invariant combination of the Lorentz terms which can be interpreted in terms of a (frame dependent) effective mass. We find that spin couplings can induce a temperature independent polarization in the gas that is not present in the conventional case.

hep-ph↗

arXiv2004

Deformed Instantons

In this talk, instantons are discussed in the presence of Lorentz violation. Conventional topological arguments are applied to classify the modified solutions to the Yang-Mills equations according to the topological charge. Explicit perturbations to the instantons are calculated in detail for the case of unit topological charge.

hep-ph↗

arXiv2004

Statistical Mechanics and Lorentz Violation

The theory of statistical mechanics is studied in the presence of Lorentz-violating background fields. The analysis is performed using the Standard-Model Extension (SME) together with a Jaynesian formulation of statistical inference. Conventional laws of thermodynamics are obtained in the presence of a perturbed hamiltonian that contains the Lorentz violating terms. As an example, properties of the nonrelativistic ideal gas are calculated in detail. To lowest order in Lorentz violation, the scalar thermodynamic variables are only corrected by a rotationally invariant combination of parameters that mimics a (frame dependent) effective mass. Spin couplings can induce a temperature independent polarization in the classical gas that is not present in the conventional case. Precision measurements in the residual expectation values of the magnetic moment of Fermi gases in the limit of high temperature may provide interesting limits on these parameters.

hep-ph↗

arXiv2004

The Lyman-alpha Forest Power Spectrum from the Sloan Digital Sky Survey

We measure the power spectrum, P_F(k,z), of the transmitted flux in the Ly-alpha forest using 3035 high redshift quasar spectra from the Sloan Digital Sky Survey. This sample is almost two orders of magnitude larger than any previously available data set, yielding statistical errors of ~0.6% and ~0.005 on, respectively, the overall amplitude and logarithmic slope of P_F(k,z). This unprecedented statistical power requires a correspondingly careful analysis of the data and of possible systematic contaminations in it. For this purpose we reanalyze the raw spectra to make use of information not preserved by the standard pipeline. We investigate the details of the noise in the data, resolution of the spectrograph, sky subtraction, quasar continuum, and metal absorption. We find that background sources such as metals contribute significantly to the total power and have to be subtracted properly. We also find clear evidence for SiIII correlations with the Ly-alpha forest and suggest a simple model to account for this contribution to the power. While it is likely that our newly developed analysis technique does not eliminate all systematic errors in the P_F(k,z) measurement below the level of the statistical errors, our tests indicate that any residual systematics in the analysis are unlikely to affect the inference of cosmological parameters from P_F(k,z). These results should provide an essential ingredient for all future attempts to constrain modeling of structure formation, cosmological parameters, and theories for the origin of primordial fluctuations.

astro-ph↗

arXiv2004

The Transverse Proximity Effect: A Probe to the Environment, Anisotropy, and Megayear Variability of QSOs

The transverse proximity effect is the expected decrease in the strength of the Lya forest absorption in a QSO spectrum when another QSO lying close to the line of sight enhances the photoionization rate above that due to the average cosmic ionizing background. We select three QSOs from the Early Data Release of the Sloan Digital Sky Survey that have nearby foreground QSOs, with proper line of sight tangential separations of 0.50, 0.82, and 1.10 h^{-1} Mpc. We estimate that the ionizing flux from the foreground QSO should increase the photoionization rate by a factor (94, 13, 13) in these three cases, which would be clearly detectable in the first QSO and marginally so in the other two. We do not detect the transverse proximity effect. Three possible explanations are provided: an increase of the gas density in the vicinity of QSOs, time variability, and anisotropy of the QSO emission. We find that the increase of gas density near QSOs can be important if they are located in the most massive halos present at high redshift, but is not enough to fully explain the absence of the transverse proximity effect. Anisotropy requires an unrealistically small opening angle of the QSO emission. Variability demands that the luminosity of the QSO with the largest predicted effect was much lower 10^6 years ago, whereas the transverse proximity effect observed in the HeII Lya absorption in QSO 0302-003 by Jakobsen et al. (2003) implies a lifetime longer than 10^7 years. A combination of all three effects may better explain the lack of Lya absorption reduction. A larger sample of QSO pairs may be used to diagnose the environment, anisotropy and lifetime distribution of QSOs.

astro-ph↗

arXiv2004

Weak Lensing and CMB: Parameter forecasts including a running spectral index

We use statistical inference theory to explore the constraints from future galaxy weak lensing (cosmic shear) surveys combined with the current CMB constraints on cosmological parameters, focusing particularly on the running of the spectral index of the primordial scalar power spectrum, $α_s$. Recent papers have drawn attention to the possibility of measuring $α_s$ by combining the CMB with galaxy clustering and/or the Lyman-$α$ forest. Weak lensing combined with the CMB provides an alternative probe of the primordial power spectrum. We run a series of simulations with variable runnings and compare them to semi-analytic non-linear mappings to test their validity for our calculations. We find that a ``Reference'' cosmic shear survey with $f_{sky}=0.01$ and $6.6\times 10^8$ galaxies per steradian can reduce the uncertainty on $n_s$ and $α_s$ by roughly a factor of 2 relative to the CMB alone. We investigate the effect of shear calibration biases on lensing by including the calibration factor as a parameter, and show that for our Reference Survey, the precision of cosmological parameter determination is only slightly degraded even if the amplitude calibration is uncertain by as much as 5%. We conclude that in the near future weak lensing surveys can supplement the CMB observations to constrain the primordial power spectrum.

astro-ph↗

arXiv2003

Cosmological constraints from the CMB and Ly-alpha forest revisited

The WMAP team has recently highlighted the usefulness of combining the Ly-alpha forest constraints with those from the cosmic microwave background (CMB). This combination is particularly powerful as a probe of the primordial shape of the power spectrum. Converting between the Ly-alpha forest observations and the linear mass power spectrum requires a careful treatment of nuisance parameters and modeling with cosmological simulations. We point out several issues which lead to an expansion of the errors, the two most important being the range of cosmological parameters explored in simulations and the treatment of the mean transmitted flux constraints. We employ a likelihood calculator for the current Ly-alpha data set based on an extensive 6-dimensional grid of simulations. We show that the current uncertainties in the mean transmission and the flux power spectrum define a degeneracy line in the amplitude-slope plane. The CMB degeneracy due to the primordial power spectrum shape follows a similar relation in this plane. This weakens the statistical significance of the primordial power spectrum shape constraints based on combined CMB+Ly-alpha forest analysis. Using the current data the simplest n=1 scale invariant model with dn/dln k=0 and no tensors has a Delta chi^2=4 compared to the best fitting model in which these 3 parameters are free. Current data therefore do not require relaxing these parameters to improve the fit.

astro-ph↗

arXiv2002

Constraining the dark energy with Ly-alpha forest

Statistical properties of gas absorption in high redshift quasars such as power spectrum and bispectrum allow one to determine the evolution of structure over the redshift range 2 0.1-0.2 at z>2. In combination with low redshift studies one can place useful limits on the time evolution of the equation of state.

astro-ph↗

arXiv2002

Moment Problems and the Causal Set Approach to Quantum Gravity

We study a collection of discrete Markov chains related to the causal set approach to modeling discrete theories of quantum gravity. The transition probabilities of these chains satisfy a general covariance principle, a causality principle, and a renormalizability condition. The corresponding dynamics are completely determined by a sequence of nonnegative real coupling constants. Using techniques related to the classical moment problem, we give a complete description of any such sequence of coupling constants. We prove a representation theorem: every discrete theory of quantum gravity arising from causal set dynamics satisfying covariance, causality and renormalizability corresponds to a unique probability distribution function on the nonnegative real numbers, with the coupling constants defining the theory given by the moments of the distribution.

gr-qc↗

arXiv2002

Diffusions on Graphs, Poisson Problems and Spectral Geometry

We study diffusions, variational principles and associated boundary value problems on directed graphs with natural weightings. Using random walks and exit times, we associate to certain subgraphs (domains) a pair of sequences, each of which is invariant under the action of the automorphism group of the underlying graph. We prove that these invariants differ by an explicit combinatorial factor given by Stirling numbers of the first and second kind. We prove that for any domain with a natural weighting, these invariants determine the eigenvalues of the Laplace operator corresponding to eigenvectors with nonzero mean. As a specific example, we investigate the relationship between our invariants and heat content asymptotics, expressing both as special values of a Dirichlet series.

math.SP↗

arXiv2002

Dirichlet Spectrum and Heat Content

Let $M$ be a complete Riemannian manifold and $D\subset M$ a smoothly bounded domain with compact closure. We use Brownian motion and the classic results on the Stieltjes moment problem to study the relationship between the Dirichlet spectrum of $D$ and the heat content asymptotics of $D.$ Central to our investigation is a sequence of invariants associated to $D$ defined using exit time moments. We prove that our invariants determine that part of the spectrum corresponding to eigenspaces which are not orthogonal to constant functions, that our invariants determine the heat content asymptotics associated to the manifold, and that when the manifold is a generic domain in Euclidean space, the invariants determine the Dirichlet spectrum.

math.SP↗

arXiv2002

Redefining Spinors in Lorentz-Violating QED

An analysis of spinor redefinitions in the context of the Lorentz-violating QED extension is performed. Certain parameters that apparently violate Lorentz invariance are found to be physically irrelevant as they can be removed from the lagrangian using an appropriate redefinition of the spinor field components. It is shown that conserved currents may be defined using a modified action of the complex extension of the Lorentz group on the redefined spinors. This implies a natural correspondence between the apparently Lorentz-violating theory and conventional QED. Redefinitions involving derivatives are shown to relate certain terms in the QED extension to lagrangians involving nonlocal interactions or skewed coordinate systems. The redundant parameters in the QED extension are identified and the lagrangian is rewritten in terms of physically relevant coupling constants. The resulting lagrangian contains only physically relevant parameters and transforms conventionally under Lorentz transformations.

hep-ph↗

arXiv2001

Large-scale Correlation of Mass and Galaxies with the Lyman-alpha Forest Transmitted Flux

We present predictions of the correlation between the Lyman-alpha forest absorption in quasar spectra and the mass within \sim 5 Mpc/h (comoving) of the line of sight, using fully hydrodynamic and hydro-PM numerical simulations of the cold dark matter model supported by present observations. The observed correlation based on galaxies and the Lya forest can be directly compared to our theoretical results, assuming that galaxies are linearly biased on large scales. Specifically, we predict the average value of the mass fluctuation, , conditioned to a fixed value of the Lya forest transmitted flux delta_F, after they have been smoothed over a 10 Mpc/h cube and line of sight interval, respectively. We find that /sigma_m as a function of delta_F/sigma_F has a slope of 0.6 at this smoothing scale, where sigma_m and sigma_F are the rms dispersions (this slope should decrease with the smoothing scale). We show that this value is largely insensitive to the cosmological model and other Lya forest parameters. Comparison of our predictions to observations should provide a fundamental test of our ideas on the nature of the Lya forest and the distribution of galaxies, and can yield a measurement of the bias factor of any type of galaxies that are observed in the vicinity of Lya forest lines of sight.

astro-ph↗