Non-Perturbative Models For The Quantum Gravitational Back-Reaction On Inflation

We consider a universe in which inflation commences because of a positive cosmological constant, the effect of which is progressively screened by the interaction between virtual gravitons that become trapped in the expansion of spacetime. Perturbative calculations have shown that screening becomes non-perturbatively large at late times. In this paper we consider effective field equations which can be evolved numerically to provide a non-perturbative description of the process. The induced stress tensor is that of an effective scalar field which is a non-local functional of the metric. We use the known perturbative result, constrained by general principles and guided by a physical description of the screening mechanism, to formulate a class of ansatze for this functional. A scheme is given for numerically evolving the field equations which result from a simple ansatz, from the beginning of inflation past the time when it ends. We find that inflation comes to a sudden end, producing a system whose equation of state rapidly approaches that of radiation. Explicit numerical results are presented.Comment: 50 pages, LaTeX 2 epsilon, 11 Postscript files, uses psfig.st

The Volume of the Past Light-Cone and the Paneitz Operator

We study a conjecture involving the invariant volume of the past light-cone from an arbitrary observation point back to a fixed initial value surface. The conjecture is that a 4th order differential operator which occurs in the theory of conformal anomalies gives $8\pi$ when acted upon the invariant volume of the past light-cone. We show that an extended version of the conjecture is valid for an arbitrary homogeneous and isotropic geometry. First order perturbation theory about flat spacetime reveals a violation of the conjecture which, however, vanishes for any vacuum solution of the Einstein equation. These results may be significant for constructing quantum gravitational observables, for quantifying the back-reaction on spacetime expansion and for alternate gravity models which feature a timelike vector field.Comment: 22 pages, no figures, 5 tables. Version 2 substantially extended to cover nonzero spatial curvature, and with simplified derivation

A Scalar Measure Of The Local Expansion Rate

We define a scalar measure of the local expansion rate based on how astronomers determine the Hubble constant. Our observable is the inverse conformal d'Alembertian acting on a unit ``standard candle.'' Because this quantity is an integral over the past lightcone of the observation point it provides a manifestly causal and covariant technique for averaging over small fluctuations. For an exactly homogeneous and isotropic spacetime our scalar gives minus one half times the inverse square of the Hubble parameter. Our proposal is that it be assigned this meaning generally and that it be employed to decide the issue of whether or not there is a significant quantum gravitational back-reaction on inflation. Several techniques are discussed for promoting the scalar to a full invariant by giving a geometrical description for the point of observation. We work out an explicit formalism for evaluating the invariant in perturbation theory. The results for two simple models are presented in subsequent papers.Comment: 25 pages, LaTeX 2 epsilon, 1 figur

Dimensionally Regulated Graviton 1-Point Function in de Sitter

We use dimensional regularization to compute the 1PI 1-point function of quantum gravity at one loop order in a locally de Sitter background. As with other computations, the result is a finite constant at this order. It corresponds to a small positive renormalization of the cosmological constant.Comment: 25 pages, LaTeX 2epsilon, uses Axodraw for one figure, revised to add some reference

Computing the Primordial Power Spectra Directly

The tree order power spectra of primordial inflation depend upon the norm-squared of mode functions which oscillate for early times and then freeze in to constant values. We derive simple differential equations for the power spectra, that avoid the need to numerically simulate the physically irrelevant phases of the mode functions. We also derive asymptotic expansions which should be valid until a few e-foldings before first horizon crossing, thereby avoiding the need to evolve mode functions from the ultraviolet over long periods of inflation.Comment: 11 pages, uses LaTex2

Improved Estimates of Cosmological Perturbations

We recently derived exact solutions for the scalar, vector and tensor mode functions of a single, minimally coupled scalar plus gravity in an arbitrary homogeneous and isotropic background. These solutions are applied to obtain improved estimates for the primordial scalar and tensor power spectra of anisotropies in the cosmic microwave background.Comment: 31 pages, 4 figures, LaTeX 2epsilon, this version corrects an embarrasing mistake (in the published version) for the parameter q_C. Affected eqns are 105, 109-110, 124, 148-153 and 155-15

Renormalization-group running of the cosmological constant and the fate of the universe

For a generic quantum field theory we study the role played by the renormalization-group (RG) running of the cosmological constant (CC) in determining the ultimate fate of the universe. We consider the running of the CC of generic origin (the vacuum energy of quantum fields and the potential energy of classical fields), with the RG scale proportional to the (total energy density$\rm{)^{1/4}}$ as the most obvious identification. Starting from the present-era values for cosmological parameters we demonstrate how the running can easily provide a negative cosmological constant, thereby changing the fate of the universe, at the same time rendering compatibility with critical string theory. We also briefly discuss the recent past in our scenario.Comment: 9 pages, 7 figures, revtex4; version to appear in PR

Nonperturbative late time asymptotics for heat kernel in gravity theory

Recently proposed nonlocal and nonperturbative late time behavior of the heat kernel is generalized to curved spacetimes. Heat kernel trace asymptotics is dominated by two terms one of which represents a trivial covariantization of the flat-space result and another one is given by the Gibbons-Hawking integral over asymptotically-flat infinity. Nonlocal terms of the effective action generated by this asymptotics might underly long- distance modifications of the Einstein theory motivated by the cosmological constant problem. New mechanisms of the cosmological constant induced by infrared effects of matter and graviton loops are briefly discussed.Comment: 22 pages, LaTeX, final version, to be published in Phys. Rev.

Back Reaction And Local Cosmological Expansion Rate

We calculate the back reaction of cosmological perturbations on a general relativistic variable which measures the local expansion rate of the Universe. Specifically, we consider a cosmological model in which matter is described by a single field. We analyze back reaction both in a matter dominated Universe and in a phase of scalar field-driven chaotic inflation. In both cases, we find that the leading infrared terms contributing to the back reaction vanish when the local expansion rate is measured at a fixed value of the matter field which is used as a clock, whereas they do not appear to vanish if the expansion rate is evaluated at a fixed value of the background time. We discuss possible implications for more realistic models with a more complicated matter sector.Comment: 7 pages, No figure

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