Symmetry breaking in general relativity

Bifurcation theory is used to analyze the space of solutions of Einstein's equations near a spacetime with symmetries. The methods developed here allow one to describe precisely how the symmetry is broken as one branches from a highly symmetric spacetime to nearby spacetimes with fewer symmetries, and finally to a generic solution with no symmetries. This phenomenon of symmetry breaking is associated with the fact that near symmetric solutions the space of solutions of Einstein's equations does not form a smooth manifold but rather has a conical structure. The geometric picture associated with this conical structure enables one to understand the breaking of symmetries. Although the results are described for pure gravity, they may be extended to classes of fields coupled to gravity, such as gauge theories. Since most of the known solutions of Einstein's equations have Killing symmetries, the study of how these symmetries are broken by small perturbations takes on considerable theoretical significance

The initial value problem and the dynamical formulation of general relativity

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Géometrie différentielle : une approche symplectique pour des théorémes de décomposition en géométrie ou relativité générale

Les théorémes de décomposition des tenseurs symétriques donnés par Ch. Barbance, Deser, Berger-Ebin, York et Moncrief peuvent tous étre obtenus á partir d'une construction générale de géométrie symplectique

The Atacama Cosmology Telescope: the stellar content of galaxy clusters selected using the Sunyaev-Zel'dovich effect

We present a first measurement of the stellar mass component of galaxy clusters selected via the Sunyaev-Zel'dovich (SZ) effect, using 3.6 um and 4.5 um photometry from the Spitzer Space Telescope. Our sample consists of 14 clusters detected by the Atacama Cosmology Telescope (ACT), which span the redshift range 0.27 < z < 1.07 (median z = 0.50), and have dynamical mass measurements, accurate to about 30 per cent, with median M500 = 6.9 x 10^{14} MSun. We measure the 3.6 um and 4.5 um galaxy luminosity functions, finding the characteristic magnitude (m*) and faint-end slope (alpha) to be similar to those for IR-selected cluster samples. We perform the first measurements of the scaling of SZ-observables (Y500 and y0) with both brightest cluster galaxy (BCG) stellar mass and total cluster stellar mass (M500star). We find a significant correlation between BCG stellar mass and Y500 (E(z)^{-2/3} DA^2 Y500 ~ M*^{1.2 +/- 0.6}), although we are not able to obtain a strong constraint on the slope of the relation due to the small sample size. Additionally, we obtain E(z)^{-2/3} DA^2 Y500 ~ M500star^{1.0 +/- 0.6} for the scaling with total stellar mass. The mass fraction in stars spans the range 0.006-0.034, with the second ranked cluster in terms of dynamical mass (ACT-CL J0237-4939) having an unusually low total stellar mass and the lowest stellar mass fraction. For the five clusters with gas mass measurements available in the literature, we see no evidence for a shortfall of baryons relative to the cosmic mean value.Comment: Accepted for publication in MNRAS; 12 pages, 10 figure

The Atacama Cosmology Telescope: Sunyaev-Zel'dovich Selected Galaxy Clusters at 148 GHz from Three Seasons of Data

[Abridged] We present a catalog of 68 galaxy clusters, of which 19 are new discoveries, detected via the Sunyaev-Zel'dovich effect (SZ) at 148 GHz in the Atacama Cosmology Telescope (ACT) survey of 504 square degrees on the celestial equator. A subsample of 48 clusters within the 270 square degree region overlapping SDSS Stripe 82 is estimated to be 90% complete for M_500c > 4.5e14 Msun and 0.15 < z < 0.8. While matched filters are used to detect the clusters, the sample is studied further through a "Profile Based Amplitude Analysis" using a single filter at a fixed \theta_500 = 5.9' angular scale. This new approach takes advantage of the "Universal Pressure Profile" (UPP) to fix the relationship between the cluster characteristic size (R_500) and the integrated Compton parameter (Y_500). The UPP scalings are found to be nearly identical to an adiabatic model, while a model incorporating non-thermal pressure better matches dynamical mass measurements and masses from the South Pole Telescope. A high signal to noise ratio subsample of 15 ACT clusters is used to obtain cosmological constraints. We first confirm that constraints from SZ data are limited by uncertainty in the scaling relation parameters rather than sample size or measurement uncertainty. We next add in seven clusters from the ACT Southern survey, including their dynamical mass measurements based on galaxy velocity dispersions. In combination with WMAP7 these data simultaneously constrain the scaling relation and cosmological parameters, yielding \sigma_8 = 0.829 \pm 0.024 and \Omega_m = 0.292 \pm 0.025. The results include marginalization over a 15% bias in dynamical mass relative to the true halo mass. In an extension to LCDM that incorporates non-zero neutrino mass density, we combine our data with WMAP7+BAO+Hubble constant measurements to constrain \Sigma m_\nu < 0.29 eV (95% C. L.).Comment: 32 pages, 21 figures To appear in J. Cosmology and Astroparticle Physic

An Introduction to Conformal Ricci Flow

We introduce a variation of the classical Ricci flow equation that modifies the unit volume constraint of that equation to a scalar curvature constraint. The resulting equations are named the Conformal Ricci Flow Equations because of the role that conformal geometry plays in constraining the scalar curvature. These equations are analogous to the incompressible Navier-Stokes equations of fluid mechanics inasmuch as a conformal pressure arises as a Lagrange multiplier to conformally deform the metric flow so as to maintain the scalar curvature constraint. The equilibrium points are Einstein metrics with a negative Einstein constant and the conformal pressue is shown to be zero at an equilibrium point and strictly positive otherwise. The geometry of the conformal Ricci flow is discussed as well as the remarkable analytic fact that the constraint force does not lose derivatives and thus analytically the conformal Ricci equation is a bounded perturbation of the classical unnormalized Ricci equation. That the constraint force does not lose derivatives is exactly analogous to the fact that the real physical pressure force that occurs in the Navier-Stokes equations is a bounded function of the velocity. Using a nonlinear Trotter product formula, existence and uniqueness of solutions to the conformal Ricci flow equations is proven. Lastly, we discuss potential applications to Perelman's proposed implementation of Hamilton's program to prove Thurston's 3-manifold geometrization conjectures.Comment: 52 pages, 1 figur

Detection of the Power Spectrum of Cosmic Microwave Background Lensing by the Atacama Cosmology Telescope

We report the first detection of the gravitational lensing of the cosmic microwave background through a measurement of the four-point correlation function in the temperature maps made by the Atacama Cosmology Telescope. We verify our detection by calculating the levels of potential contaminants and performing a number of null tests. The resulting convergence power spectrum at 2-degree angular scales measures the amplitude of matter density fluctuations on comoving length scales of around 100 Mpc at redshifts around 0.5 to 3. The measured amplitude of the signal agrees with Lambda Cold Dark Matter cosmology predictions. Since the amplitude of the convergence power spectrum scales as the square of the amplitude of the density fluctuations, the 4-sigma detection of the lensing signal measures the amplitude of density fluctuations to 12%.Comment: 4 pages, 4 figures, replaced title and author list with version accepted by Physical Review Letters. Likelihood code can be downloaded from http://bccp.lbl.gov/~sudeep/ACTLensLike.htm

A measurement of the millimetre emission and the Sunyaev-Zel'dovich effect associated with low-frequency radio sources

We present a statistical analysis of the millimetre-wavelength properties of 1.4GHz-selected sources and a detection of the Sunyaev–Zel’dovich (SZ) effect associated with the haloes that host them. We stack data at 148, 218 and 277GHz from the Atacama Cosmology Telescope at the positions of a large sample of radio AGN selected at 1.4GHz. The thermal SZ effect associated with the haloes that host the AGN is detected at the 5σ level through its spectral signature, representing a statistical detection of the SZ effect in some of the lowest mass haloes (average M 200 ≈ 10 13 M. h −1 70 ) studied to date. The relation between the SZ effect and mass (based on weak lensing measurements of radio galaxies) is consistent with that measured by Planck for local bright galaxies. In the context of galaxy evolution models, this study confirms that galaxies with radio AGN also typically support hot gaseous haloes. Adding Herschel observations allows us to show that the SZ signal is not significantly contaminated by dust emission. Finally, we analyse the contribution of radio sources to the angular power spectrum of the cosmic microwave background

The Atacama Cosmology Telescope: Dusty Star-Forming Galaxies and Active Galactic Nuclei in the Southern Survey

We present a catalog of 191 extragalactic sources detected by the Atacama Cosmology Telescope (ACT) at 148 GHz and/or 218 GHz in the 2008 Southern survey. Flux densities span 14-1700 mJy, and we use source spectral indices derived using ACT-only data to divide our sources into two sub-populations: 167 radio galaxies powered by central active galactic nuclei (AGN), and 24 dusty star-forming galaxies (DSFGs). We cross-identify 97% of our sources (166 of the AGN and 19 of the DSFGs) with those in currently available catalogs. When combined with flux densities from the Australian Telescope 20 GHz survey and follow-up observations with the Australia Telescope Compact Array, the synchrotron-dominated population is seen to exhibit a steepening of the slope of the spectral energy distribution from 20 to 148 GHz, with the trend continuing to 218 GHz. The ACT dust-dominated source population has a median spectral index of 3.7+0.62-0.86, and includes both local galaxies and sources with redshifts as great as 5.6. Dusty sources with no counterpart in existing catalogs likely belong to a recently discovered subpopulation of DSFGs lensed by foreground galaxies or galaxy groups.Comment: 13 pages, 8 figures, 4 table