arXiv subjects

R. P. Woodard

Publications and source records attributed to R. P. Woodard.

At least 19 recordsLinked to original sources

arXiv2026

Universal Secular External Leg Corrections for Gauge Independent Scalar Self-Mass on de Sitter

This work concerns a procedure for removing gauge dependence from graviton corrections to the effective field equations for a massless, minimally coupled scalar on de Sitter background. The procedure involves combining diagrams in the same way as the scattering amplitude for the $t$-channel exchange of the massless scalar between two massive particles, but {\it without} taking the asymptotic limits which are problematic in cosmology. Implementing this at 1-loop on flat space background requires five classes of diagrams, in addition to the naive exchange, and the combination of those diagrams does eliminate dependence on the graviton gauge fixing functional. When those same diagrams are generalized to de Sitter background, their combination cancels the most important (``nonlocal'') secular gauge dependence, but it leaves (``local'') secular gauge dependence that is associated with external legs. Local secular gauge dependence can be removed by adding two additional classes of diagrams, and making secular corrections to the external wavefunctions. The purpose of this paper is to include these additional corrections on de Sitter background in order to derive fully gauge independent effective field equations at 1-loop order.

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arXiv2026

Sub-Leading Logarithms for Scalar Potential Models on de Sitter

The continual production of long wavelength scalars and gravitons during inflation injects secular growth into loop corrections which would be constant in flat space. One typically finds that each additional factor of the loop counting parameter can induce up to a certain number of logarithms of the scale factor. Loop corrections that attain this number are known as ``leading logarithms''; those with fewer are sub-leading. Starobinsky's stochastic formalism has long been known to reproduce the leading logarithms of scalar potential models. We show that the first sub-leading logarithm is captured by applying the stochastic formalism to a certain part of the 1-loop effective potential. This is checked at 2-loops for a massless, minimally coupled scalar with a quartic self-interaction on de Sitter background.

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arXiv2026

Comments on Entire Functions of the Derivative Operator

Many attempts to introduce fundamental nonlocality into quantum (or classical) field theory are based on the assumption that exponentials of the d'Alembertian are positive-definite, so that these operators can be employed without engendering the Ostrogradskian instability associated with higher derivative Lagrangians. {\bf This assumption is false.} Working in the simple context of a 1-dimensional, point particle $q(t)$, I demonstrate that the equation $\exp[T^2 \tfrac{d^2}{dt^2}] q(t) = 0$ has an infinite number of rapidly oscillating, exponentially rising and falling solutions. This infinite kernel is in one-to-one correspondence with the ability to specify ``initial value data'' {\it arbitrarily} over {\it any} finite interval $t_1 < t < t_2$.

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arXiv2026

Sensing the Inflationary Production of Scalars

We review the mechanism by which loops of matter fields contribute to the graviton self-energy during de Sitter inflation. The self-energy is used to quantum-correct the linearized Einstein equations. A Green's function method is employed to obtain exact 1-loop corrections to the plane wave mode functions of gravitational radiation, subject to the usual ambiguity in the initial state. Conformally coupled matter, which does not experience inflationary particle production, makes only a logarithmic enhancement of the rate at which the imaginary part of the mode function goes to zero after horizon crossing. These corrections can be understood, and even summed up, using a variant of the renormalization group. However, massless, minimally coupled scalars, which experience massive inflationary particle production, induce a much stronger enhancement of the rate at which the real part of the mode function approaches a constant. One interpretation of this effect is as a shift of the inflationary Hubble parameter.

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arXiv2026

Quantum Cosmology in Accelerating Spacetimes II

This paper is a sequel in which we further analyze the recently derived quantum gravity equations which apply in accelerating cosmological spacetimes and whose solutions should be equivalent to all order re-summations of the perturbative leading logarithms that appear. In particular we study their implications concerning the primordial tensor power spectrum and the gravitational force due to a test source.

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arXiv2026

A Nonlocal Realization of MOND that Interpolates from Cosmology to Gravitationally Bound Systems

Nonlocal modifications of gravity derive from corrections to the quantum gravitational stress tensor which grow nonperturbatively strong during primordial inflation and may persist to the current epoch. Phenomenological constructions have been given that realize MOND in gravitationally bound systems and, separately, reproduce all the cosmological phenomena usually ascribed to dark matter, including the cosmic microwave background radiation, baryon acoustic oscillations and linearized structure formation. In this work we exhibit a single model that interpolates between the two regimes.

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arXiv2025

Quantum Cosmology in Accelerating Spacetimes

We simplify the gravitational equations which apply in accelerating spacetimes and are consistent with the cosmological principle. Solutions to these equations should be tantamount to all order re-summations of the perturbative leading logarithms. We discuss the null hypothesis and we study the local expansion rate observable.

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arXiv2025

Leading Logarithm Quantum Gravity II

This paper is a sequel in which we derive and simplify the gravitational equations that apply in accelerating cosmological spacetimes. Solutions to these equations should be tantamount to all order resummations of the perturbative leading logarithms. We also discuss possible phenomenological applications to cosmological observables.

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arXiv2025

The Third Structure Function

We re-consider the graviton self-energy induced by a loop of massless, minimally coupled scalars on de Sitter background. On flat space background it can be represented as a sum of two tensor differential operators acting on scalar structure functions. On a general background these tensor differential operators can be constructed from the linearized Ricci scalar and the linearized Weyl tensor. However, in cosmology one requires a third contribution which we derive here.

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arXiv2025

Recent Developments in Stochastic Inflation

This article is dedicated to the memory of Alexei Starobinsky. I begin with some recollections of him and then review the generalization of his wonderful stochastic formalism from scalar potential models to theories which interact with fermions and photons, and finally to theories with derivative interactions such as nonlinear sigma models and gravity. This entails effective potentials generated by the usual field-dependent masses, as well as by field-dependent field strengths, and by field-dependent Hubble parameters. I also discuss secular loop corrections which cannot be captured by stochastic techniques.

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arXiv2025

Resummations for Inflationary Quantum Gravity

The continual production of gravitons during inflation endows loop corrections with secular logarithms which grow nonperturbatively large during a prolonged period of inflation. The physics behind these effects is reviewed, along with a catalog of the examples which have so far been found. Resummation can be accomplished by combining a variant of Starobinsky's stochastic formalism with a variant of the renormalization group. The issue of gauge independence is also addressed.

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arXiv2024

Resumming Fermion Loops for Inflationary Gravity

We compute the 1-loop contribution to the graviton self-energy from a loop of massless fermions on a general cosmological background. The result is used to quantum-correct the linearized Einstein equation on de Sitter background and work out 1-loop corrections to gravitational radiation and to the response to a point mass. The renormalization group is employed to sum these to all orders for as long as the de Sitter phase persists.

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arXiv2024

Resumming Photon Loops for Inflationary Gravity

A previous calculation of the 1-loop photon contribution to the graviton self-energy on de Sitter background is considered. We first show that there is no local obstacle to conservation, unlike the contribution from a loop of massless, minimally coupled scalars. This is correlated to the absence of an Eddington ($R^2$) counterterm and to the vanishing of the stress tensor when the photon in integrated out in the presence of a constant graviton field. We also show that there is a secularly growing 1-loop contribution to the electric components of the Weyl tensor for plane wave gravitons. Its coefficient agrees with that of the secular 1-loop correction to the Newtonian potential, and both can be resummed using a variant of the renormalization group.

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arXiv2024

The Other ADM

In the peculiar manner by which physicists reckon descent, this article is by a "child" and "grandchild" of the late Stanley Deser. We begin by sharing reminiscences of Stanley from over 40 years. Then we turn to a problem which was dear to his heart: the prospect that gravity might nonperturbatively screen its own ultraviolet divergences and those of other theories. After reviewing the original 1960 work by ADM, we describe a cosmological analogue of the problem and then begin the process of implementing it in gravity plus QED.

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arXiv2024

Summing Gravitational Effects from Loops of Inflationary Scalars

We develop a procedure for re-summing the large logarithms induced in gravity by loops of inflationary scalars. We first show how the scalar can be integrated out of the field equations in the presence of constant graviton field. We then extend this result to a fully conserved form which explains the need for a finite renormalization of the cosmological constant which was previously inferred from explicit computation. A variant of the renormalization group turns out to explain the large logarithmic corrections revealed by explicit computation in the electric field strength of gravitational radiation and in the potentials which characterize the response to a point mass. The implications for graviton loops are discussed.

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arXiv2024

Leading Logarithm Quantum Gravity

The continual production of long wavelength gravitons during primordial inflation endows graviton loop corrections with secular growth factors. During a prolonged period of inflation these factors eventually overwhelm the small loop-counting parameter of $G H^2$, causing perturbation theory to break down. A technique was recently developed for summing the leading secular effects at each order in non-linear sigma models, which possess the same kind of derivative interactions as gravity. This technique combines a variant of Starobinsky's stochastic formalism with a variant of the renormalization group. We generalize the new technique to quantum gravity, resulting in a Langevin equation in which secular changes in gravitational phenomena are driven by stochastic fluctuations of the graviton field.

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arXiv2024

Alternate Computation of Gravitational Effects from a Single Loop of Inflationary Scalars

We present a new computation of the renormalized graviton self-energy induced by a loop of massless, minimally coupled scalars on de Sitter background. Our result takes account of the need to include a finite renormalization of the cosmological constant, which was not included in the first analysis. We also avoid preconceptions concerning structure functions and instead express the result as a linear combination of 21 tensor differential operators. By using our result to quantum-correct the linearized effective field equation we derive logarithmic corrections to both the electric components of the Weyl tensor for gravitational radiation and to the two potentials which quantify the gravitational response to a static point mass.

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arXiv2024

The Price of Abandoning Dark Matter Is Nonlocality

We consider the classic question posed by Pardo and Spergel about the price of abandoning dark matter in the context of an invariant, metric-based theory of gravity. Our answer is that the price is nonlocality. This has been known for some time in the context of the quasi-static regime. We show that it also applies for cosmology and we exhibit a model which reproduces standard CDM successes such as perturbations in the cosmic microwave background, baryon acoustic oscillations and structure formation.

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