One Loop Graviton Self-Energy In A Locally De Sitter Background

The graviton tadpole has recently been computed at two loops in a locally de Sitter background. We apply intermediate results of this work to exhibit the graviton self-energy at one loop. This quantity is interesting both to check the accuracy of the first calculation and to understand the relaxation effect it reveals. In the former context we show that the self-energy obeys the appropriate Ward identity. We also show that its flat space limit agrees with the flat space result obtained by Capper in what should be the same gauge.Comment: 35 pages, plain TeX, 4 Postscript files, uses psfig.sty, revised June 1996 for publication in Physical Review

The Quantum Gravitationally Induced Stress Tensor

We derive non-perturbative relations between the expectation value of the invariant element in a homogeneous and isotropic state and the quantum gravitationally induced pressure and energy density. By exploiting previously obtained bounds for the maximum possible growth of perturbative corrections to a locally de Sitter background we show that the two loop result dominates all higher orders. We also show that the quantum gravitational slowing of inflation becomes non-perturbatively strong earlier than previously expected.Comment: 13 pages, LaTeX 2 epsilo

One Loop Back Reaction On Power Law Inflation

We consider quantum mechanical corrections to a homogeneous, isotropic and spatially flat geometry whose scale factor expands classically as a general power of the co-moving time. The effects of both gravitons and the scalar inflaton are computed at one loop using the manifestly causal formalism of Schwinger with the Feynman rules recently developed by Iliopoulos {\it et al.} We find no significant effect, in marked contrast with the result obtained by Mukhanov {\it et al.} for chaotic inflation based on a quadratic potential. By applying the canonical technique of Mukhanov {\it et al.} to the exponential potentials of power law inflation, we show that the two methods produce the same results, within the approximations employed, for these backgrounds. We therefore conclude that the shape of the inflaton potential can have an enormous impact on the one loop back-reaction.Comment: 28 pages, LaTeX 2 epsilo

General plane wave mode functions for scalar-driven cosmology

We give a solution for plane wave scalar, vector and tensor mode functions in the presence of any homogeneous, isotropic and spatially flat cosmology which is driven by a single, minimally coupled scalar. The solution is obtained by rescaling the various mode functions so that they reduce, with a suitable scale factor and a suitable time variable, to those of a massless, minimally coupled scalar. We then express the general solution in terms of co-moving time and the original scale factor.Comment: 6 pages, revtex4, no figures, revised version corrects an embarrassing mistake (in the published version) for the parameter q_C. Affected eqns are 45 and 6

One Loop Back Reaction On Chaotic Inflation

We extend, for the case of a general scalar potential, the inflaton-graviton Feynman rules recently developed by Iliopoulos {\it et al.} As an application we compute the leading term, for late co-moving times, of the one loop back reaction on the expansion rate for $V(\phi) = \frac12 m^2 \phi^2$. This is expressed as the logarithmic time derivative of the scale factor in the coordinate system for which the expectation value of the metric has the form: $dx^{\mu} dx^{\nu} = - d{\bar t}^2 + a^2({\bar t}) d{\vec x} \cdot d{\vec x}$. This quantity should be a gauge independent observable. Our result for it agrees exactly with that inferred from the effect previously computed by Mukhanov {\it et al.} using canonical quantization. It is significant that the two calculations were made with completely different schemes for fixing the gauge, and that our computation was done using the standard formalism of covariant quantization. This should settle some of the issues recently raised by Unruh.Comment: 41 pages, LaTeX 2 epsilo

Charged Scalar Self-Mass during Inflation

We compute the one loop self-mass of a charged massless, minimally coupled scalar in a locally de Sitter background geometry. The computation is done in two different gauges: the noninvariant generalization of Feynman gauge which gives the simplest expression for the photon propagator and the de Sitter invariant gauge of Allen and Jacobson. In each case dimensional regularization is employed and fully renormalized results are obtained. By using our result in the linearized, effective field equations one can infer how the scalar responds to the dielectric medium produced by inflationary particle production. We also work out the result for a conformally coupled scalar. Although the conformally coupled case is of no great physical interest the fact that we obtain a manifestly de Sitter invariant form for its self-mass-squared establishes that our noninvariant gauge introduces no physical breaking of de Sitter invariance at one loop order.Comment: 41 pages, LaTeX 2epsilon, 3 figures, uses axodra

Plane waves in a general Robertson-Walker background

We present an exact solution for the plane wave mode functions of a massless, minimally coupled scalar propagating in an arbitrary homogeneous, isotropic and spatially flat geometry. Our solution encompasses all previous solvable special cases such as de Sitter and power law expansion. Moreover, it can generate the mode functions for gravitons. We discuss some of the many applications that are now possible.Comment: 11 pages, revtex4, no figures, version 3 is vastly expanded (from 57 eqns to 166) to give an explicit expression for the transfer matrix, and to expand it in the ultraviolet and the infrared. We use the infrared limit to give an improved result for the gravitational wave contribution to CMB anisotropie

Electron temperature fluctuations in NGC 346

The existence and origin of large spatial temperature fluctuations in HII regions and planetary nebulae are assumed to explain the differences between the heavy element abundances inferred from collisionally excited and recombination lines, although this interpretation remains significantly controversial. We investigate the spatial variation in electron temperature inside NGC 346, the brightest HII region in the Small Magellanic Cloud. Long slit spectrophotometric data of high signal-to-noise were employed to derive the electron temperature from measurements derived from localized observations of the [OIII]($\lambda4959 + \lambda5007)/\lambda4363$ ratio in three directions across the nebula. The electron temperature was estimated in 179 areas of 5$^{\prime\prime}\times1.5^{\prime\prime}$ of size distributed along three different declinations. A largely homogeneous temperature distribution was found with a mean temperature of 12 269 K and a dispersion of 6.1%. After correcting for pure measurements errors, a temperature fluctuation on the plane of the sky of $t^2_{\rm s} = 0.0021$ (corresponding to a dispersion of 4.5%) was obtained, which indicates a 3D temperature fluctuation parameter of $t^2 \approx 0.008$. A large scale gradient in temperature of the order of $-5.7\pm1.3$ K arcsec$^{-1}$ was found. The magnitude of the temperature fluctuations observed agrees with the large scale variations in temperature predicted by standard photoionization models, but is too small to explain the abundance discrepancy problem. However, the possible existence of small spatial scale temperature variations is not excluded.Comment: 6 pages, 5 figures, 2 table

High order correlation functions for self interacting scalar field in de Sitter space

We present the expressions of the three- and four-point correlation functions of a self interacting light scalar field in a de Sitter spacetime at tree order respectively for a cubic and a quartic potential. Exact expressions are derived and their limiting behaviour on super-horizon scales are presented. Their essential features are shown to be similar to those obtained in a classical approach.Comment: 8 pages, 4 figure

Role of a "Local" Cosmological Constant in Euclidean Quantum Gravity

In 4D non-perturbative Regge calculus a positive value of the effective cosmological constant characterizes the collapsed phase of the system. If a local term of the form $S'=\sum_{h \epsilon \{h_1,h_2,...\} } \lambda_h V_h$ is added to the gravitational action, where $\{h_1,h_2,...\}$ is a subset of the hinges and $\{\lambda_h\}$ are positive constants, one expects that the volumes $V_{h_1}$, $V_{h_2}$, ... tend to collapse and that the excitations of the lattice propagating through the hinges $\{h_1,h_2,...\}$ are damped. We study the continuum analogue of this effect. The additional term $S'$ may represent the coupling of the gravitational field to an external Bose condensate.Comment: LaTex, 18 page