Adiabatic Modes in Cosmology

We show that the field equations for cosmological perturbations in Newtonian gauge always have an adiabatic solution, for which a quantity ${\cal R}$ is non-zero and constant in all eras in the limit of large wavelength, so that it can be used to connect observed cosmological fluctuations in this mode with those at very early times. There is also a second adiabatic mode, for which ${\cal R}$ vanishes for large wavelength, and in general there may be non-adiabatic modes as well. These conclusions apply in all eras and whatever the constituents of the universe, under only a mild technical assumption about the wavelength dependence of the field equations for large wave length. In the absence of anisotropic inertia, the perturbations in the adiabatic modes are given for large wavelength by universal formulas in terms of the Robertson--Walker scale factor. We discuss an apparent discrepancy between these results and what appears to be a conservation law in all modes found for large wavelength in synchronous gauge: it turns out that, although equivalent, synchronous and Newtonian gauges suggest inequivalent assumptions about the behavior of the perturbations for large wavelength.Comment: 24 pages, Latex, no special macro

Fluctuating geometries, q-observables, and infrared growth in inflationary spacetimes

Infrared growth of geometrical fluctuations in inflationary spacetimes is investigated. The problem of gauge-invariant characterization of growth of perturbations, which is of interest also in other spacetimes such as black holes, is addressed by studying evolution of the lengths of curves in the geometry. These may either connect freely falling "satellites," or wrap non-trivial cycles of geometries like the torus, and are also used in diffeomorphism- invariant constructions of two-point functions of field operators. For spacelike separations significantly exceeding the Hubble scale, no spacetime geodesic connects two events, but one may find geodesics constrained to lie within constant-time spatial slices. In inflationary geometries, metric perturbations produce significant and growing corrections to the lengths of such geodesics, as we show in both quantization on an inflating torus and in standard slow-roll inflation. These become large, signaling breakdown of a perturbative description of the geometry via such observables, and consistent with perturbative instability of de Sitter space. In particular, we show that the geodesic distance on constant time slices during inflation becomes non-perturbative a few e-folds after a given scale has left the horizon, by distances \sim 1/H^3 \sim RS, obstructing use of such geodesics in constructing IR-safe observables based on the spatial geometry. We briefly discuss other possible measures of such geometrical fluctuations.Comment: 33 pages, 2 figures, latex; v2: typos corrected, references improve

Flavor Changing Scalar Interactions

The smallness of fermion masses and mixing angles has recently been been attributed to approximate global $U(1)$ symmetries, one for each fermion type. The parameters associated with these symmetry breakings are estimated here directly from observed masses and mixing angles. It turns out that although flavor changing reaction rates may be acceptably small in electroweak theories with several scalar doublets without imposing any special symmetries on the scalars themselves, such theories generically yield too much CP violation in the neutral kaon mass matrix. Hence in these theories CP must also be a good approximate symmetry. Such models provide an alternative mechanism for CP violation and have various interesting phenomenological features.Comment: 18 pages. UTTG-22-92; LBL 33016; UCB 92/3

Extension of the Chiral Perturbation Theory Meson Lagrangian to Order P6P^6

We have derived the most general chirally invariant Lagrangian ${\cal L}_6$ for the meson sector at order $p^6$. The result provides an extension of the standard Gasser-Leutwyler Lagrangian ${\cal L}_4$ to one higher order, including as well all the odd intrinsic parity terms in the Lagrangian. The most difficult part of the derivation was developing a systematic strategy so as to get all of the independent terms and eliminate the redundant ones in an efficient way. The 'equation of motion' terms, which are redundant in the sense that they can be transformed away via field transformations, are separated out explicitly. The resulting Lagrangian has been separated into groupings of terms contributing to increasingly more complicated processes, so that one does not have to deal with the full result when calculating $p^6$ contributions to simple processes.Comment: 59 pages in LaTex, using RevTex macro, TRIUMF preprint TRI-PP-94-6

Constraints on Lorentz invariance violation from gamma-ray burst GRB090510

We obtain modified dispersion relations by requiring the vanishing of determinant of inverse of modified photon propagators in Lorentz invariance violation (LIV) theory. Inspired by these dispersion relations, we give a more general dispersion relation with less assumption and apply it to the recent observed gamma-ray burst GRB090510 to extract various constraints on LIV parameters. We find that the constraint on quantum gravity mass is slightly larger than the Planck mass but is consistent with the other recent observations, so the corresponding LIV coefficient $\xi_1$ has reached the natural order ($o(1)$) as one expects. From our analysis, the linear LIV corrections to photon group velocity might be not excluded yet.Comment: 10 latex pages, no figures, version accepted for publication in PR

Perspective on gravitational self-force analyses

A point particle of mass $\mu$ moving on a geodesic creates a perturbation $h_{ab}$, of the spacetime metric $g_{ab}$, that diverges at the particle. Simple expressions are given for the singular $\mu/r$ part of $h_{ab}$ and its distortion caused by the spacetime. This singular part h^\SS_{ab} is described in different coordinate systems and in different gauges. Subtracting h^\SS_{ab} from $h_{ab}$ leaves a regular remainder $h^\R_{ab}$. The self-force on the particle from its own gravitational field adjusts the world line at \Or(\mu) to be a geodesic of $g_{ab}+h^\R_{ab}$; this adjustment includes all of the effects of radiation reaction. For the case that the particle is a small non-rotating black hole, we give a uniformly valid approximation to a solution of the Einstein equations, with a remainder of \Or(\mu^2) as $\mu\to0$. An example presents the actual steps involved in a self-force calculation. Gauge freedom introduces ambiguity in perturbation analysis. However, physically interesting problems avoid this ambiguity.Comment: 40 pages, to appear in a special issue of CQG on radiation reaction, contains additional references, improved notation for tensor harmonic

Effective Field Theories in the Large NN Limit

Various effective field theories in four dimensions are shown to have exact non-trivial solutions in the limit as the number $N$ of fields of some type becomes large. These include extended versions of the U(N) Gross-Neveu model, the non-linear O(N) $\sigma$-model, and the $CP^{N-1}$ model. Although these models are not renormalizable in the usual sense, the infinite number of coupling types allows a complete cancellation of infinities. These models provide qualitative predictions of the form of scattering amplitudes for arbitrary momenta, but because of the infinite number of free parameters, it is possible to derive quantitative predictions only in the limit of small momenta. For small momenta the large-$N$ limit provides only a modest simplification, removing at most a finite number of diagrams to each order in momenta, except near phase transitions, where it reduces the infinite number of diagrams that contribute for low momenta to a finite number.Comment: 48 pages, no figures. This is a plain LaTeX file. No special macros are neede

Efficient Computation of Casimir Interactions between Arbitrary 3D Objects

We introduce an efficient technique for computing Casimir energies and forces between objects of arbitrarily complex 3D geometries. In contrast to other recently developed methods, our technique easily handles non-spheroidal, non-axisymmetric objects and objects with sharp corners. Using our new technique, we obtain the first predictions of Casimir interactions in a number of experimentally relevant geometries, including crossed cylinders and tetrahedral nanoparticles.Comment: 4 pages, 4 figure

A Validated Method for Identifying Unplanned Pediatric Readmission

Objective To validate the accuracy of pre-encounter hospital designation as a novel way to identify unplanned pediatric readmissions and describe the most common diagnoses for unplanned readmissions among children. Study design We examined all hospital discharges from 2 tertiary care children's hospitals excluding deaths, normal newborn discharges, transfers to other institutions, and discharges to hospice. We performed blinded medical record review on 641 randomly selected readmissions to validate the pre-encounter planned/unplanned hospital designation. We identified the most common discharge diagnoses associated with subsequent 30-day unplanned readmissions. Results Among 166 994 discharges (hospital A: n = 55 383; hospital B: n = 111 611), the 30-day unplanned readmission rate was 10.3% (hospital A) and 8.7% (hospital B). The hospital designation of “unplanned” was correct in 98% (hospital A) and 96% (hospital B) of readmissions; the designation of “planned” was correct in 86% (hospital A) and 85% (hospital B) of readmissions. The most common discharge diagnoses for which unplanned 30-day readmissions occurred were oncologic conditions (up to 38%) and nonhypertensive congestive heart failure (about 25%), across both institutions. Conclusions Unplanned readmission rates for pediatrics, using a validated, accurate, pre-encounter designation of “unplanned,” are higher than previously estimated. For some pediatric conditions, unplanned readmission rates are as high as readmission rates reported for adult conditions. Anticipating unplanned readmissions for high-frequency diagnostic groups may help focus efforts to reduce the burden of readmission for families and facilities. Using timing of hospital registration in administrative records is an accurate, widely available, real-time way to distinguish unplanned vs planned pediatric readmissions