arXiv subjects

R. P. Woodard

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

At least 55 records · Page 3Linked to original sources

arXiv2021

Inflaton Effective Potential from Photons for General $ε$

We accurately approximate the contribution that photons make to the effective potential of a charged inflaton for inflationary geometries with an arbitrary first slow roll parameter $ε$. We find a small, nonlocal contribution and a numerically larger, local part. The local part involves first and second derivatives of $ε$, coming exclusively from the constrained part of the electromagnetic field which carries the long range interaction. This causes the effective potential induced by electromagnetism to respond more strongly to geometrical evolution than for either scalars, which have no derivatives, or spin one half particles, which have only one derivative. For $ε= 0$ our final result agrees with that of Allen on de Sitter background, while the flat space limit agrees with the classic result of Coleman and Weinberg.

gr-qc↗

arXiv2021

One-loop Graviton Corrections to Conformal Scalars on a de Sitter Background

We exploit a recent computation of one graviton loop corrections to the self-mass [1] to quantum-correct the field equation for a massless, conformally coupled scalar on a de Sitter background. With the obvious choice for the finite part of the $R^2 ϕ^2$ counterterm, we find that neither plane wave mode functions nor the response to a point source acquires large infrared logarithms. However, we do find a decaying logarithmic correction to the mode function and a short distance logarithmic running of the potential in addition to the power-law effect inherited from flat space.

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arXiv2020

Bose-Fermi Cancellation of Cosmological Coleman-Weinberg Potentials

Cosmological Coleman-Weinberg potentials are induced when normal matter is coupled to the inflaton. It has long been known that the corrections from bosonic fields are positive whereas those from fermionic fields are negative. In flat space both take the form $\pm φ^4 \ln(φ)$, and they can be made to cancel by appropriately choosing the coupling constants. In an expanding universe the bosonic and fermionic results no longer take the same form, although their large field limits do. We choose the coupling constants so that the large field limits cancel, and then follow the deviations which result as inflation progresses. Although the result is not satisfactory we discuss how adding scalars with various conformal couplings likely solves the problem.

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arXiv2020

The Inflaton Effective Potential for General $ε$

We develop an analytic approximation for the coincidence limit of a massive scalar propagator in an arbitrary spatially flat, homogeneous and isotropic geometry. We employ this to compute the one loop corrections to the inflaton effective potential from a quadratic coupling to a minimally coupled scalar. We also extend the Friedmann equations to cover potentials that depend locally on the Hubble parameter and the first slow roll parameter.

gr-qc↗

arXiv2020

Single Graviton Loop Contribution to the Self-Mass of a Massless, Conformally Coupled Scalar on de Sitter Background

We use a simplified formalism to re-compute the single graviton loop contribution to the self-mass of a massless, conformally coupled scalar on de Sitter background which was originally made by Boran, Kahya and Park [1-3]. Our result resolves the problem with the flat space correspondence limit that was pointed out by Fröb [4]. We discuss how this computation will be used in a long-term project to purge the linearized effective field equation of gauge dependence.

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arXiv2019

Ricci Subtraction for Cosmological Coleman-Weinberg Potentials

We reconsider the fine-tuning problem of scalar-driven inflation arising from the need to couple the inflaton to ordinary matter in order to make reheating efficient. Quantum fluctuations of this matter induce Coleman-Weinberg corrections to the inflaton potential, depending (for de Sitter background) in a complex way on the ratio of the inflaton to the Hubble parameter. These corrections are not Planck-suppressed and cannot be completely subtracted because they are not even local for a general geometry. A previous study showed that it is not satisfactory to subtract a local function of just the inflaton and the {\it initial} Hubble parameter. This paper examines the other allowed possibility of subtracting a local function of the inflaton and the Ricci scalar. The problem in this case is that the new, scalar degree of freedom induced by the subtraction causes inflation to end almost instantly.

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arXiv2019

Breaking of scaling symmetry by massless scalar on de Sitter

We study the response of a classical massless minimally coupled scalar to a static point scalar charge on de Sitter. By considering explicit solutions of the problem we conclude that -- even though the dynamics formally admits dilatation (scaling) symmetry -- the physical scalar field profile necessarily breaks the symmetry. This is an instance of symmetry breaking in classical physics due to large infrared effects. The gravitational backreaction, on the other hand, does respect dilatation symmetry, making this an example of symmetry non-inheritance phenomenon.

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arXiv2019

Graviton Propagator in a 2-Parameter Family of de Sitter Breaking Gauges

We formulate the graviton propagator on de Sitter background in a 2-parameter family of simple gauges which break de Sitter invariance. Explicit results are derived for the first order perturbations in each parameter. These results should be useful in computations to check for gauge dependence of graviton loop corrections.

gr-qc↗

arXiv2019

Non-Gaussianity from Features

The strongest non-Gaussianity in single-scalar potential models of inflation is associated with features in the power spectrum. We stress the importance of accurately modelling the expected signal in order for the standard estimator to minimize contamination by random noise. We present explicit formulae which improve on the approximation introduced by Adshead, Hu, Dvorkin and Peiris. We also compare with a simple, analytic model of the first feature, and quantify our results using the correlators of Hung, Fergusson and Shellard.

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arXiv2019

Nonlocal Cosmology II --- Cosmic acceleration without fine tuning or dark energy

We present an improved version of our original cosmological model to explain the current phase of cosmological acceleration without resorting to a cosmological constant or any other mass scale. Like the original, this phenomenological approach is based on an effective quantum gravitational action, but now depends on the original nonlocal dimensionless scalar $X = \square^{-1} R$ only through $Y = \square^{-1} g^{μν} X_{,μ} X_{,ν}$. Both $X$ and $Y$ are quiescent during the radiation-dominated ($R=0$) era, both only grow logarithmically during matter dominance, and neither affects the propagation of gravitational radiation. However, while $X$ has the same sign for gravitationally bound systems as for cosmology, we show that the sign of $Y$ differs for the two cases: it is positive for cosmology and negative for strongly gravitationally bound systems. We can therefore enforce the $Λ$CDM expansion history by making a suitable choice of the nonlocal distortion function $f(Y)$ for $Y > 0$, while ensuring that there is no change in the heavily constrained solar system phenomenology simply by making $f$ vanish for $Y < 0$ without discontinuity. The required $f(Y>0)$ is determined numerically to have a strikingly simple exponential form.

gr-qc↗

arXiv2019

Cosmological Coleman-Weinberg Potentials and Inflation

We consider an additional fine-tuning problem which afflicts scalar-driven models of inflation. The problem is that successful reheating requires the inflaton be coupled to ordinary matter, and quantum fluctuations of this matter induces Coleman-Weinberg potentials which are not Planck-suppressed. Unlike the flat space case, these potentials depend upon a still-unknown, nonlocal functional of the metric which reduces to the Hubble parameter for de Sitter. Such a potential cannot be completely subtracted off by any local action. In a simple model we numerically consider one possible subtraction scheme in which the correction is locally subtracted at the beginning of inflation. For fermions the effect is to make the universe approach de Sitter with a smaller Hubble parameter. For gauge bosons the effect is to make inflation end almost instantly unless the gauge charge is unacceptably small.

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arXiv2019

Do the Spirits Rise?

A nonlocal gravity model based on $\frac1{\square} R$ achieves the phenomenological goals of generating cosmic acceleration without dark energy and of suppressing the growth of perturbations compared to the $Λ$CDM model. Although the localized version of this model possesses a scalar ghost, the nonlocal version does not suffer from any obvious problem with ghosts. Here we study the possibility that the scalar ghost mode might be excited through time evolution, even though it is initially absent. We present strong evidence that this does not happen.

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arXiv2018

The Case for Nonlocal Modifications of Gravity

The huge amounts of undetected and exotic dark matter and dark energy needed to make general relativity work on large scales argue that we should investigate modifications of gravity. The only stable, metric-based and invariant alternative to general relativity is $f(R)$ models. These models can explain primordial inflation, but they cannot dispense with either dark matter or dark energy. I advocate nonlocal modifications of gravity, not as new fundamental theories but rather as the gravitational vacuum polarization engendered by infrared quanta produced during primordial inflation. I also discuss some of the many objections which have been raised to this idea.

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arXiv2018

The Graviton Tail almost Completely Wags the Dog

One graviton loop corrections to the vacuum polarization on de Sitter show two interesting infrared effects: a secular enhancement of the photon electric field strength and a long range running of the Coulomb potential. We show that the first effect derives solely from the "tail" term of the graviton propagator, but that the second effect does not. Our result agrees with the earlier observation that the secular enhancement of massless fermion mode functions derives from solely from the tail term. We discuss the implications this has for the important project of generalizing to quantum gravity the Starobinsky technique for summing the series of leading infrared effects from inflationary quantum field theory.

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arXiv2018

Structure Formation in Nonlocal MOND

We consider structure formation in a nonlocal, metric-based realization of Milgrom's MOdified Newtonian Dynamics (MOND). We derive the general equations for linearized scalar perturbations about the $Λ$CDM expansion history. These equations are considerably simplified for sub-horizon modes, and it becomes obvious (in this model) that the MOND enhancement is not sufficient to allow ordinary matter to drive structure formation. We discuss ways in which the model might be changed to correct the problem.

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arXiv2017

From Non-trivial Geometries to Power Spectra and Vice Versa

We review a recent formalism which derives the functional forms of the primordial -- tensor and scalar -- power spectra of scalar potential inflationary models. The formalism incorporates the case of geometries with non-constant first slow-roll parameter. Analytic expressions for the power spectra are given that explicitly display the dependence on the geometric properties of the background. Moreover, we present the full algorithm for using our formalism, to reconstruct the model from the observed power spectra. Our techniques are applied to models possessing "features" in their potential with excellent agreement.

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arXiv2017

Improving the Single Scalar Consistency Relation

We propose a test of single-scalar inflation based on using the well-measured scalar power spectrum to reconstruct the tensor power spectrum, up to a single integration constant. Our test is a sort of integrated version of the single-scalar consistency relation. This sort of test can be used effectively, even when the tensor power spectrum is measured too poorly to resolve the tensor spectral index. We give an example using simulated data based on a hypothetical detection with tensor-to-scalar ratio $r = 0.01$. Our test can also be employed for correlating scalar and tensor features in the far future when the data is good.

astro-ph.CO↗

arXiv2017

Precision Predictions for the Primordial Power Spectra of Scalar Potential Models of Inflation

We exploit a new numerical technique for evaluating the tree order contributions to the primordial scalar and tensor power spectra for scalar potential models of inflation. Among other things we use the formalism to develop a good analytic approximation which goes beyond generalized slow roll expansions in that (1) it is not contaminated by the physically irrelevant phase, (2) its 0th order term is exact for constant first slow roll parameter, and (3) the correction is multiplicative rather than additive. These features allow our formalism to capture at first order, effects which are higher order in other expansions. Although this accuracy is not necessary to compare current data with any specific model, our method has a number of applications owing to the simpler representation it provides for the connection between the power spectra and the expansion history of a general model.

astro-ph.CO↗