arXiv subjects

R. P. Woodard

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

At least 91 records · Page 5Linked to original sources

arXiv2014

Electrodynamic Effects of Inflationary Gravitons

We calculate the one-loop corrections from inflationary gravitons to the electromagnetic fields of a point charge and a point magnetic dipole on a locally de Sitter space background. Results are obtained both for an observer at rest in co-moving coordinates, whose physical distance from the sources increases with the expanding universe, and for an observer at rest in static coordinates, whose physical distance from the sources is constant. The fields of both sources show the de Sitter analogs of the fractional $G/r^2$ corrections which occur in flat space, but there are also some fractional $G H^2$ corrections due to the scattering of virtual photons from the vast ensemble of infrared gravitons produced by inflation. The co-moving observer perceives the magnitude of the point charge to increase linearly with co-moving time and logarithmically with the co-moving position, however, the magnetic dipole shows only a negative logarithmic spatial variation. The static observer perceives no secular change of the point charge but he does report a secular enhancement of the magnetic dipole moment.

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arXiv2014

Representing the Graviton Self-Energy on de Sitter Background

We derive a noncovariant but simple representation for the self-energy of a conformally transformed graviton field on the cosmological patch of de Sitter. Our representation involves four structure functions, as opposed to the two that would be necessary for a manifestly de Sitter invariant representation. We work out what the four structure functions are for the one loop correction due to a massless, minimally coupled scalar. And we employ the result to work out what happens to dynamical gravitons.

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arXiv2014

Perturbative Quantum Gravity Comes of Age

I argue that cosmological data from the epoch of primordial inflation is catalyzing the maturation of quantum gravity from speculation into a hard science. I explain why quantum gravitational effects from primordial inflation are observable. I then review what has been done, both theoretically and observationally, and what the future holds. I also discuss what this tells us about quantum gravity.

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arXiv2014

Graviton Corrections to Vacuum Polarization during Inflation

We use dimensional regularization to compute the one loop quantum gravitational contribution to the vacuum polarization on de Sitter background. Adding the appropriate BPHZ counterterms gives a fully renormalized result which can be used to quantum correct Maxwell's equations. We use the Hartree approximation to argue that the electric field strengths of photons experience a secular suppression during inflation.

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arXiv2014

Classical Gravitational Back-Reaction

The quantum gravitational back-reaction on inflation is based on the self-gravitation of infrared gravitons which are ripped out of the vacuum during inflation. The only quantum part of this process is the creation of gravitons; after they have emerged from the vacuum their behaviour is essentially classical. To test the thesis that a sufficiently dense ensemble of classical gravitons can hold the universe together in pure gravity with a positive cosmological constant, we compute the initial value and first time derivative of an invariant measure of the expansion rate for arbitrary classical initial value data. Our result is that the self-gravitation from the kinetic energy of an initial ensemble of gravitons can indeed slow expansion enough to hold the universe together.

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arXiv2014

A Caveat on Building Nonlocal Models of Cosmology

Nonlocal models of cosmology might derive from graviton loop corrections to the effective field equations from the epoch of primordial inflation. Although the Schwinger-Keldysh formalism would automatically produce causal and conserved effective field equations, the models so far proposed have been purely phenomenological. Two techniques have been employed to generate causal and conserved field equations: either varying an invariant nonlocal effective action and then enforcing causality by the ad hoc replacement of any advanced Green's function with its retarded counterpart, or else introducing causal nonlocality into a general ansatz for the field equations and then enforcing conservation. We point out here that the two techniques access very different classes of models, and that neither one of them may represent what would actually arise from fundamental theory.

astro-ph.CO↗

arXiv2014

The Perils of Analytic Continuation

A nice paper by Morrison demonstrates the recent convergence of opinion that has taken place concerning the graviton propagator on de Sitter background. We here discuss the few points which remain under dispute. First, the inevitable decay of tachyonic scalars really does result in their 2-point functions breaking de Sitter invariance. This is obscured by analytic continuation techniques which produce formal solutions to the propagator equation that are not propagators. Second, Morrison's de Sitter invariant solution for the spin two sector of the graviton propagator involves derivatives of the scalar propagator at $M^2 = 0$, where it is not meromorphic unless de Sitter breaking is permitted. Third, de Sitter breaking does not require zero modes. Fourth, the ambiguity Morrison claims in the equation for the spin two structure function is fixed by requiring it to derive from a mode sum. Fifth, Morrison's spin two sector is not "physically equivalent" to ours because their coincidence limits differ. Finally, it is only the noninvariant propagator that gets the time independence and scale invariance of the tensor power spectrum correctly.

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arXiv2014

Nonlocal Metric Realizations of MOND

I discuss relativistic extensions of MOND in which the metric couples normally to matter. I argue that MOND might be a residual effect from the vacuum polarization of infrared gravitons produced during primordial inflation. If so, MOND corrections to the gravitational field equations would be nonlocal. Nonocality also results when one constructs metric field equations which reproduce the Tully-Fisher relation, along with sufficient weak lensing. I give the full field equations for the simplest class of models, and I specialize these equations to the geometries relevant for cosmology. I conclude by sketching the direction of future studies.

astro-ph.CO↗

arXiv2014

Nonlocal Models of Cosmic Acceleration

I review a class of nonlocally modified gravity models which were proposed to explain the current phase of cosmic acceleration without dark energy. Among the topics considered are deriving causal and conserved field equations, adjusting the model to make it support a given expansion history, why these models do not require an elaborate screening mechanism to evade solar system tests, degrees of freedom and kinetic stability, and the negative verdict of structure formation. Although these simple models are not consistent with data on the growth of cosmic structures many of their features are likely to carry over to more complicated models which are in better agreement with the data.

astro-ph.CO↗

arXiv2013

Observational Viability and Stability of Nonlocal Cosmology

We show that a class of nonlocal gravity models, proposed to explain current cosmic acceleration without dark energy, passes two major tests: First, they can be defined so as not to alter the, observationally correct, general relativity predictions for gravitationally bound systems. Second, they are stable, ghost-free, with no additional excitations beyond those of general relativity. In this they differ from their, ghostful, localized versions. The systems' initial value constraints are the same as in general relativity, and our nonlocal modifications never convert the original gravitons into ghosts.

astro-ph.CO↗

arXiv2013

Hartree Approximation to the One Loop Quantum Gravitational Correction to the Graviton Mode Function on de Sitter

We use the Hartree approximation to the Einstein equation on de Sitter background to solve for the one loop correction to the graviton mode function. This should give a reasonable approximation to how the ensemble of inflationary gravitons affects a single external graviton. At late times we find that the one loop correction to the plane wave mode function $u(η,k)$ goes like $G H^2 \ln(a)/a^2$, where $a$ is the inflationary scale factor. One consequence is that the one loop corrections to the "electric" components of the linearized Weyl tensor grow compared to the tree order result.

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arXiv2013

Pure Gravitational Back-Reaction Observables

After discussing the various issues regarding and requirements on pure quantum gravitational observables in homogeneous-isotropic conditions, we construct a composite operator observable satisfying most of them. We also expand it to first order in the loop counting parameter and suggest it as a physical quantifier of gravitational back-reaction in an initially inflating cosmology.

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arXiv2013

One Loop Field Strengths of Charges and Dipoles on a Locally de Sitter Background

We use the one loop vacuum polarization induced by scalar quantum electrodynamics to compute the electric and magnetic fields of point charges and magnetic dipoles on a locally de Sitter background. Our results are consistent with the physical picture of an inflating universe filling with a vast sea of charged particles as more and more virtual infrared scalar are ripped out of the vacuum. One consequence is that vacuum polarization quickly becomes nonperturbatively strong. Our computation employs the Schwinger-Keldysh effective field equations and is done in flat, conformal coordinates. Results are also obtained for static coordinates.

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arXiv2012

Representing the Vacuum Polarization on de Sitter

Previous studies of the vacuum polarization on de Sitter have demonstrated that there is a simple, noncovariant representation of it in which the physics is transparent. There is also a cumbersome, covariant representation in which the physics is obscure. Despite being unwieldy, the latter form has a powerful appeal for those who are concerned about de Sitter invariance. We show that nothing is lost by employing the simple, noncovariant representation because there is a closed form procedure for converting its structure functions to those of the covariant representation. We also present a vastly improved technique for reading off the noncovariant structure functions from the primitive diagrams. And we discuss the issue of representing the vacuum polarization for a general metric background.

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arXiv2012

Covariant Vacuum Polarizations on de Sitter Background

We derive covariant expressions for the one loop vacuum polarization induced by a charged scalar on de Sitter background. Two forms are employed: one in which two covariant derivatives act on de Sitter invariant basis tensors multiplied by scalar structure functions, and the other in which four covariant derivatives act on a single basis tensor times a structure function. The second representation permits the correction to dynamical photons to be expressed as a surface integral, which raises the important question of what sorts of effects can be absorbed into corrections of the initial state. Results are obtained for charged, minimally coupled scalars which are either massless or else light. The former show de Sitter breaking whereas the latter are de Sitter invariant. However, the de Sitter invariant formulation does not seem useful, even when it is possible. Our work has important implications for representations of the graviton self-energy on de Sitter.

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arXiv2012

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.

astro-ph.CO↗

arXiv2012

Issues Concerning Loop Corrections to the Primordial Power Spectra

We expound ten principles in an attempt to clarify the debate over infrared loop corrections to the primordial scalar and tensor power spectra from inflation. Among other things we note that existing proposals for nonlinear extensions of the scalar fluctuation field $ζ$ introduce new ultraviolet divergences which no one understands how to renormalize. Loop corrections and higher correlators of these putative observables would also be enhanced by inverse powers of the slow roll parameter $ε$. We propose an extension which should be better behaved.

astro-ph.CO↗

arXiv2012

Graviton Corrections to Maxwell's Equations

We use dimensional regularization to compute the one loop quantum gravitational contribution to the vacuum polarization on flat space background. Adding the appropriate BPHZ counterterm gives a fully renormalized result which we employ to quantum correct Maxwell's equations. These equations are solved to show that dynamical photons are unchanged, provided the free state wave functional is appropriately corrected. The response to the instantaneous appearance of a point dipole reveals a perturbative version of the long-conjectured, "smearing of the light-cone". There is no change in the far radiation field produced by an alternating dipole. However, the correction to the static electric field of a point charge shows strengthening at short distances, in contrast to expectations based on the renormalization group. We check for gauge dependence by working out the vacuum polarization in a general 3-parameter family of covariant gauges.

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