arXiv subjects

R. P. Woodard

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

At least 37 records · Page 2Linked to original sources

arXiv2024

Gauge Independent Logarithms from Inflationary Gravitons

Dependence on the graviton gauge enters the conventional effective field equations because they fail to account for quantum gravitational correlations with the source which excites the effective field and with the observer who measures it. Including these correlations has been shown to eliminate gauge dependence in flat space background. We generalize the technique to de Sitter background for the case of the 1-loop graviton corrections to the exchange potential of a massless, minimally coupled scalar.

hep-th↗

arXiv2023

The Need to Renormalize the Cosmological Constant

We consider the massless, minimally coupled scalar on de Sitter background. Although the 1-loop divergences of the graviton 1PI 2-point function are canceled by the usual Weyl ($C^2$) and Eddington ($R^2$) counterterms, there is still a finite, nonzero contribution to the graviton 1-point function. Unless this is canceled by a finite renormalization of the cosmological constant, the 1PI 2-point function will not be conserved, nor will the parameter ``$H$'' correspond to the actual Hubble constant. We argue that a similar finite renormalization of the cosmological constant is necessary in pure gravity, and that this must be done when solving the effective field equations for 1-loop corrections to the graviton wave function and to the force of gravity.

gr-qc↗

arXiv2023

Large Inflationary Logarithms in a Nontrivial Nonlinear Sigma Model

Loops of inflationary gravitons are known to induce large temporal and spatial logarithms which can cause perturbation theory to break down. Nonlinear sigma models possess the same kind of derivative interactions and induce the same sorts of large logarithms, without the complicated index structure and potential gauge problem. Previous studies have examined models with zero field space curvature which can be reduced to free field theories by local, invertible field redefinitions. Here we study a model which cannot be so reduced and still shows the same sorts of large logarithms. We compute the evolution of the background at 1-loop and 2-loop orders, and we find the 1-loop $β$ and $γ$ functions.

gr-qc↗

arXiv2023

Explaining Large Electromagnetic Logarithms from Loops of Inflationary Gravitons

Recent progress on nonlinear sigma models on de Sitter background has permitted the resummation of large inflationary logarithms by combining a variant of Starobinsky's stochastic formalism with a variant of the renormalization group. We reconsider single graviton loop corrections to the photon wave function, and to the Coulomb potential, in light of these developments. Neither of the two 1-loop results have a stochastic explanation, however, the flow of a curvature-dependent field strength renormalization explains their factors of $\ln(a)$. We speculate that the factor of $\ln(Hr)$ in the Coulomb potential should not be considered as a leading logarithm effect.

gr-qc↗

arXiv2023

Remembrance of Things Past

Nonlinear sigma models on de Sitter background have proved a useful prototype for quantum gravity in summing the large logarithms which arise from loop corrections. We consider a model whose evolution is described, at leading logarithm order, by the trace of the coincident, doubly differentiated scalar propagator. An analytic approximation for this quantity on an arbitrary expansion history is applied to generalize the resummed de Sitter result to any cosmological background which has experienced primordial inflation. In addition to analytic expressions, we present explicit numerical results for the evolution in a plausible expansion history. The large scales of primordial inflation are transmitted to late times.

gr-qc↗

arXiv2023

Unfinished Business in A Nonlinear Sigma Model on de Sitter Background

Nonlinear sigma models on de Sitter background possess the same kind of derivative interactions as gravity, and show the same sorts of large spacetime logarithms in correlation functions and solutions to the effective field equations. It was recently demonstrated that these logarithms can be resummed by combining a variant of Starobinsky's stochastic formalism with a variant of the renormalization group. This work considers one of these models and completes two pieces of analysis which were left unfinished: the evolution of the background at two loop order and the one loop beta function.

gr-qc↗

arXiv2023

Don't Throw the Baby Out with the Bath Water

I stress the importance of retaining a healthy classical limit while we search for an ultraviolet completion to quantum gravity. A key problem with negative-norm quantizations of higher derivative Lagrangians is that their classical limits do not correspond to real-valued metrics evolving in a real-valued spacetime. I also demonstrate that no completion based on the flat spacetime background S-matrix can suffice by providing an explicit example of a theory with unit S-matrix which still shows interesting changes in single-particle kinematics and in the evolution of its background. I discuss the implications of these considerations for the program of Asymptotic Safety. Finally, I urge that some attention be given to the possibility that quantum general relativity might make sense if only we could go beyond conventional perturbation theory.

gr-qc↗

arXiv2023

Coincident Massless, Minimally Coupled Scalar Correlators on General Cosmological Backgrounds

The coincidence limits of the massless, minimally coupled scalar propagator and its first two derivatives have great relevance for the project of summing up the leading logarithms induced by loops of inflationary gravitons. We use dimensional regularization to derive good analytic approximations for the three quantities on a general cosmological background geometry which underwent inflation.

gr-qc↗

arXiv2023

Perturbative Quantum Gravity Induced Scalar Coupling to Electromagnetism

Physicists working on atom interferometers are interested in scalar couplings to electromagnetism of dimensions 5 and 6 which might be induced by quantum gravity. There is a widespread belief that such couplings can only be induced by conjectured non-perturbative effects, resulting in unknown coupling strengths. In this letter we exhibit a completely perturbative mechanism through which quantum gravity induces dimension six couplings with precisely calculable coefficients.

gr-qc↗

arXiv2023

Big Steve and the State of the Universe

I share some reminiscences of the late Steven Weinberg. Then I discuss a topic in quantum field theory which he taught me: the role of state wave functionals in deriving the $iε$ term of the Feynman propagator when using the functional formalism. This is perhaps a curiosity for in-out scattering amplitudes on flat space backgrounds, but it is has much greater significance for the in-in amplitudes of the Schwinger-Keldysh formalism in cosmology. It also touches on the fate, about which Weinberg wondered, of the large logarithms one sometimes finds in quantum corrections from inflationary particle production.

hep-th↗

arXiv2022

Reheating with Effective Potentials

We consider reheating for a charged inflaton which is minimally coupled to electromagnetism. The evolution of such an inflaton induces a time-dependent mass for the photon. We show how the massive photon propagator can be expressed as a spatial Fourier mode sum involving three different sorts of mode functions, just like the constant mass case. We develop accurate analytic approximations for these mode functions, and use them to approximate the effective force exerted on the inflaton $0$-mode. This effective force allows one to simply compute the evolution of the inflaton $0$-mode and to follow the progress of reheating.

hep-ph↗

arXiv2022

How Inflationary Gravitons Affect the Force of Gravity

We employ an unregulated computation the graviton self-energy from gravitons on de Sitter background to infer the renormalized result. This is used to quantum-correct the linearized Einstein equation. We solve this equation for the potentials which represent the gravitational response to static, point mass. We find large spatial and temporal logarithmic corrections to the Newtonian potential and to the gravitational shift. Although suppressed by a minuscule loop-counting parameter, these corrections cause perturbation theory to break down at large distances and late times. Another interesting fact is that gravitons induce up to three large logarithms whereas a loop of massless, minimally coupled scalars produces only a single large logarithm. This is in line with corrections to the graviton mode function: a loop of gravitons induces two large logarithms whereas a scalar loop gives none.

gr-qc↗

arXiv2022

How Inflationary Gravitons Affect Gravitational Radiation

We include the single graviton loop contribution to the linearized Einstein equation. Explicit results are obtained for one loop corrections to the propagation of gravitational radiation. Although suppressed by a minuscule loop-counting parameter, these corrections are enhanced by the square of the number of inflationary e-foldings. One consequence is that perturbation theory breaks down for a very long epoch of primordial inflation. Another consequence is that the one loop correction to the tensor power spectrum might be observable, in the far future, after the full development of 21cm cosmology.

gr-qc↗

arXiv2022

Large Logarithms from Quantum Gravitational Corrections to a Massless, Minimally Coupled Scalar on de Sitter

We consider single graviton loop corrections to the effective field equation of a massless, minimally coupled scalar on de Sitter background in the simplest gauge. We find a large temporal logarithm in the approach to freeze-in at late times, but no correction to the feeze-in amplitude. We also find a large spatial logarithm (at large distances) in the scalar potential generated by a point source, which can be explained using the renormalization group with one of the higher derivative counterterms regarded as a curvature-dependent field strength renormalization. We discuss how these results set the stage for a project to purge gauge dependence by including quantum gravitational corrections to the source which disturbs the effective field and to the observer who measures it.

gr-qc↗

arXiv2022

Summing Inflationary Logarithms in Nonlinear Sigma Models

We consider two nonlinear sigma models on de Sitter background which involve the same derivative interactions as quantum gravity but without the gauge issue. The first model contains only a single field, which can be reduced to a free theory by a local field redefinition; the second contains two fields and cannot be so reduced. Loop corrections in both models produce large temporal and spatial logarithms which cause perturbation theory to break down at late times and large distances. Many of these logarithms derive from the "tail" part of the propagator and can be summed using a variant of Starobinsky's stochastic formalism involving a curvature-dependent effective potential. The remaining logarithms derive from the ultraviolet and can be summed using a variant of the renormalization group based on a special class of curvature-dependent renormalizations. Explicit results are derived at 1-loop and 2-loop orders.

gr-qc↗

arXiv2021

Gauge Independent Quantum Gravitational Corrections to Maxwell's Equation

We consider quantum gravitational corrections to Maxwell's equations on flat space background. Although the vacuum polarization is highly gauge dependent, we explicitly show that this gauge dependence is canceled by contributions from the source which disturbs the effective field and the observer who measures it. Our final result is a gauge independent, real and causal effective field equation that can be used in the same way as the classical Maxwell equation.

gr-qc↗

arXiv2021

Inflaton Effective Potential from Fermions for General $ε$

We accurately approximate the contribution of a Yukawa-coupled fermion to the inflaton effective potential for inflationary geometries with a general first slow roll parameter $ε(t)$. For $ε= 0$ our final result agrees with the famous computation of Candelas and Raine done long ago on de Sitter background, and both computations degenerate to the result of Coleman and Weinberg in the flat space limit. Our result contains a small part that depends nonlocally on the inflationary geometry. Even in the numerically larger local part, very little of the $ε$ dependence takes the form of Ricci scalars. We discuss the implications of these corrections for inflation.

gr-qc↗

arXiv2021

Graviton Self-Energy from Gravitons in Cosmology

Although matter contributions to the graviton self-energy $-i[\mbox{}^{μν} Σ^{ρσ}](x;x')$ must be separately conserved on $x^μ$ and ${x'}^μ$, graviton contributions obey the weaker constraint of the Ward identity, which involves a divergence on both coordinates. On a general homogeneous and isotropic background this leads to just four structure functions for matter contributions but nine structure functions for graviton contributions. We propose a convenient parameterization for these nine structure functions. We also apply the formalism to explicit one loop computations of $-i[\mbox{}^{μν} Σ^{ρσ}](x;x')$ on de Sitter background, one of the contributions from a massless, minimally coupled scalar and the other for the contribution from gravitons in the simplest gauge. We also specialize the linearized, quantum-corrected Einstein equation to the graviton mode function and to the gravitational response to a point mass.

gr-qc↗