Local phase space and edge modes for diffeomorphism-invariant theories

We discuss an approach to characterizing local degrees of freedom of a subregion in diffeomorphism-invariant theories using the extended phase space of Donnelly and Freidel, [JHEP 2016 (2016) 102]. Such a characterization is important for defining local observables and entanglement entropy in gravitational theories. Traditional phase space constructions for subregions are not invariant with respect to diffeomorphisms that act at the boundary. The extended phase space remedies this problem by introducing edge mode fields at the boundary whose transformations under diffeomorphisms render the extended symplectic structure fully gauge invariant. In this work, we present a general construction for the edge mode symplectic structure. We show that the new fields satisfy a surface symmetry algebra generated by the Noether charges associated with the edge mode fields. For surface-preserving symmetries, the algebra is universal for all diffeomorphism-invariant theories, comprised of diffeomorphisms of the boundary, $SL(2,\mathbb{R})$ transformations of the normal plane, and, in some cases, normal shearing transformations. We also show that if boundary conditions are chosen such that surface translations are symmetries, the algebra acquires a central extension.Comment: 29+12 pages, references added and minor typos fixe

Non-linear Redshift-Space Power Spectra

Distances in cosmology are usually inferred from observed redshifts - an estimate that is dependent on the local peculiar motion - giving a distorted view of the three dimensional structure and affecting basic observables such as the correlation function and power spectrum. We calculate the full non-linear redshift-space power spectrum for Gaussian fields, giving results for both the standard flat sky approximation and the directly-observable angular correlation function and angular power spectrum. Coupling between large and small scale modes boosts the power on small scales when the perturbations are small. On larger scales power is slightly suppressed by the velocities perturbations on smaller scales. The analysis is general, but we comment specifically on the implications for future high-redshift observations, and show that the non-linear spectrum has significantly more complicated angular structure than in linear theory. We comment on the implications for using the angular structure to separate cosmological and astrophysical components of 21 cm observations.Comment: 22 pages, 6 figures, changed to version accepted in Physics Review

Improving CMB non-Gaussianity estimators using tracers of local structure

Local non-Gaussianity causes correlations between large scale perturbation modes and the small scale power. The large-scale CMB signal has contributions from the integrated Sachs Wolfe (ISW) effect, which does not correlate with the small scale power. If this ISW contribution can be removed, the sensitivity to local non-Gaussianity is improved. Gravitational lensing and galaxy counts can be used to trace the ISW contribution; in particular we show that the CMB lensing potential is highly correlated with the ISW signal. We construct a nearly-optimal estimator for the local non-Gaussianity parameter \fnl and investigate to what extent we can use this to decrease the variance on {\fnl}. We show that the variance can be decreased by up to $20\%$ at Planck sensitivity using galaxy counts. CMB lensing is a good bias-independent ISW tracer for future more sensitive observations, though the fractional decrease in variance is small if good polarization data is also available.Comment: 8 pages, 3 figures. Comments welcom

Massive neutrinos and magnetic fields in the early universe

Primordial magnetic fields and massive neutrinos can leave an interesting signal in the CMB temperature and polarization. We perform a systematic analysis of general perturbations in the radiation-dominated universe, accounting for any primordial magnetic field and including leading-order effects of the neutrino mass. We show that massive neutrinos qualitatively change the large-scale perturbations sourced by magnetic fields, but that the effect is much smaller than previously claimed. We calculate the CMB power spectra sourced by inhomogeneous primordial magnetic fields, from before and after neutrino decoupling, including scalar, vector and tensor modes, and consistently modeling the correlation between the density and anisotropic stress sources. In an appendix we present general series solutions for the possible regular primordial perturbations

Multigrid solution of the Navier-Stokes equations on triangular meshes

A Navier-Stokes algorithm for use on unstructured triangular meshes is presented. Spatial discretization of the governing equations is achieved using a finite element Galerkin approximation, which can be shown to be equivalent to a finite volume approximation for regular equilateral triangular meshes. Integration steady-state is performed using a multistage time-stepping scheme, and convergence is accelerated by means of implicit residual smoothing and an unstructured multigrid algorithm. Directional scaling of the artificial dissipation and the implicit residual smoothing operator is achieved for unstructured meshes by considering local mesh stretching vectors at each point. The accuracy of the scheme for highly stretched triangular meshes is validated by comparing computed flat-plate laminar boundary layer results with the well known similarity solution, and by comparing laminar airfoil results with those obtained from various well-established structured quadrilateral-mesh codes. The convergence efficiency of the present method is also shown to be competitive with those demonstrated by structured quadrilateral-mesh algorithms