Deducing Cosmological Observables from the S-matrix

We study one loop quantum gravitational corrections to the long range force induced by the exchange of a massless scalar between two massive scalars. The various diagrams contributing to the flat space S-matrix are evaluated in a general covariant gauge and we show that dependence on the gauge parameters cancels at a point considerably {\it before} forming the full S-matrix, which is unobservable in cosmology. It is possible to interpret our computation as a solution to the effective field equations --- which could be done even in cosmology --- but taking account of quantum gravitational corrections from the source and from the observer.Comment: 28 pages, 5 figures, uses LaTeX2

The Graviton Tail almost Completely Wags the Dog

One graviton loop corrections to the vacuum polarization on de Sitter show two interesting infrared effects: a secular enhancement of the photon electric field strength and a long range running of the Coulomb potential. We show that the first effect derives solely from the "tail" term of the graviton propagator, but that the second effect does not. Our result agrees with the earlier observation that the secular enhancement of massless fermion mode functions derives from solely from the tail term. We discuss the implications this has for the important project of generalizing to quantum gravity the Starobinsky technique for summing the series of leading infrared effects from inflationary quantum field theory.Comment: 17 pages, 1 figure, uses LaTeX2

Pair creation and axial anomaly in light-cone QED2QED_2

The 1+1 dimensional massive Dirac equation is solved exactly in light-cone coordinates for $x^+ > 0$ and $x^- > -L$, in the presence of an arbitrary $x^+$ dependent electric field. Our solution resolves the ambiguity at $p^+ = 0$. We also obtain the one loop rate for pair production for a positive electric field, compute the expectation values of the vector and axial vector currents, and recover the well known anomaly $e^2 E/\pi$ in the divergence of the latter. A final intriguing result is that the theory seems to exhibit a phase transition in the limit of infinite $L$.Comment: 33 pages, 2 figures, LaTeX 2 epsilon, revised for publicatio

Two Loop Scalar Bilinears for Inflationary SQED

We evaluate the one and two loop contributions to the expectation values of two coincident and gauge invariant scalar bilinears in the theory of massless, minimally coupled scalar quantum electrodynamics on a locally de Sitter background. One of these bilinears is the product of two covariantly differentiated scalars, the other is the product of two undifferentiated scalars. The computations are done using dimensional regularization and the Schwinger-Keldysh formalism. Our results are in perfect agreement with the stochastic predictions at this order.Comment: 43 pages, LaTeX 2epsilon, 5 figures (using axodraw.sty) Version 2 has updated references and important corrections to Tables 3-5 and to eqns (139-141), (145-146), (153-155), (158) and (160

A Simple Operator Check of the Effective Fermion Mode Function during Inflation

We present a relatively simple operator formalism which reproduces the leading infrared logarithm of the one loop quantum gravitational correction to the fermion mode function on a locally de Sitter background. This rule may serve as the basis for an eventual stochastic formulation of quantum gravity during inflation. Such a formalism would not only effect a vast simplification in obtaining the leading powers of $\ln(a)$ at fixed loop orders, it would also permit us to sum the series of leading logarithms. A potentially important point is that our rule does not seem to be consistent with any simple infrared truncation of the fields. Our analysis also highlights the importance of spin as a gravitational interaction that persists even when kinetic energy has redshifted to zero.Comment: 39 pages, no figuire.(1) New version has clarified the ultimate motivation by adding sentences to the abstract and to the penultimate paragraph of the introduction. (2) By combining a number of references and equations we have managed to reduce the length by 2 page

Quality assessment of two- and three-dimensional unstructured meshes and validation of an upwind Euler flow solver

Quality assessment procedures are described for two-dimensional and three-dimensional unstructured meshes. The procedures include measurement of minimum angles, element aspect ratios, stretching, and element skewness. Meshes about the ONERA M6 wing and the Boeing 747 transport configuration are generated using an advancing front method grid generation package of programs. Solutions of Euler's equations for these meshes are obtained at low angle-of-attack, transonic conditions. Results for these cases, obtained as part of a validation study demonstrate the accuracy of an implicit upwind Euler solution algorithm

Single Graviton Loop Contribution to the Self-Mass of a Massless, Conformally Coupled Scalar on de Sitter Background

We use a simplified formalism to re-compute the single graviton loop contribution to the self-mass of a massless, conformally coupled scalar on de Sitter background which was originally made by Boran, Kahya and Park [1-3]. Our result resolves the problem with the flat space correspondence limit that was pointed out by Fr\"ob [4]. We discuss how this computation will be used in a long-term project to purge the linearized effective field equation of gauge dependence.Comment: 26 pages, 1 figure, uses LaTeX 2e. Version 2 revised slightly for publicatio

Leading Log Solution for Inflationary Yukawa

We generalize Starobinskii's stochastic technique to the theory of a massless, minimally coupled scalar interacting with a massless fermion in a locally de Sitter geometry. The scalar is an ``active'' field that can engender infrared logarithms. The fermion is a ``passive'' field that cannot cause infrared logarithms but which can carry them, and which can also induce new interactions between the active fields. The procedure for dealing with passive fields is to integrate them out, then stochastically simplify the resulting effective action following Starobinski\u{\i}. Because Yukawa theory is quadratic in the fermion this can be done explicitly using the classic solution of Candelas and Raine. We check the resulting stochastic formulation against an explicit two loop computation. We also derive a nonperturbative, leading log result for the stress tensor. Because the scalar effective potential induced by fermions is unbounded below, back-reaction from this model might dynamically cancel an arbitrarily large cosmological constant.Comment: 35 pages, LaTeX 2epsilon, 4 figures (using axodraw), version 2 has an updated reference lis