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R. P. Woodard

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

At least 163 records · Page 9Linked to original sources
arXiv2004

Quantum effects can render w<-1 on cosmological scales

We report on a revision of our previous computation of the renormalized expectation value of the stress-energy tensor of a massless, minimally coupled scalar with a quartic self-interaction on a locally de Sitter background. This model is important because it demonstrates that quantum effects can lead to violations of the weak energy condition on cosmological scales - on average, not just in fluctuations - although the effect in this particular model is far too small to be observed. The revision consists of modifying the propagator so that dimensional regularization can be used when the dimension of the renormalized theory is not four. Although the finite part of the stress-energy tensor does not change (in D=4) from our previous result, the counterterms do. We also speculate that a certain, finite and separately conserved part of the stress tensor can be subsumed into a natural correction of the initial state from free Bunch-Davies vacuum.

gr-qc↗
arXiv2004

General plane wave mode functions for scalar-driven cosmology

We give a solution for plane wave scalar, vector and tensor mode functions in the presence of any homogeneous, isotropic and spatially flat cosmology which is driven by a single, minimally coupled scalar. The solution is obtained by rescaling the various mode functions so that they reduce, with a suitable scale factor and a suitable time variable, to those of a massless, minimally coupled scalar. We then express the general solution in terms of co-moving time and the original scale factor.

astro-ph↗
arXiv2004

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.

astro-ph↗
arXiv2003

Quantum Effects during Inflation

The expansion of spacetime alters the energy-time uncertainty principle, allowing virtual particles to persist longer than in flat space. For a given expansion the effect is largest for massless particles which are not conformally invariant. For a given particle type the effect is largest for inflation. I exhibit these two principles in the context of massless fermions which are Yukawa-coupled to massless scalars. I also review the many related examples which have been studied recently.

astro-ph↗
arXiv2003

A generic problem with purely metric formulations of MOND

We give a simple argument to show that no purely metric-based, relativistic formulation of Milgrom's Modified Newtonian Dynamics (MOND) whose energy functional is stable (in the sense of being quadratic in perturbations) can be consistent with the observed amount of gravitational lensing from galaxies. An important part of the argument is the fact that reproducing the MOND force law requires any completely stable, metric-based theory of gravity to become conformally invariant in the weak field limit. We discuss the prospects for a formulation with a very weak instability.

astro-ph↗
arXiv2003

Fermion Self-Energy during Inflation

I report on work done with Tomislav Prokopec (Heidelberg, CERN). We computed the one loop self-energy of a massless fermion during inflation. When the fermion is free it experiences only a small amount of inflationary particle production owing to the conformal invariance of its classical action. However, when the fermion is Yukawa coupled to a massless, minimally coupled scalar, there is copious production of fermions. In a more complicated model this effect might generate baryon asymmetry during inflation.

astro-ph↗
arXiv2003

Plane waves in a general Robertson-Walker background

We present an exact solution for the plane wave mode functions of a massless, minimally coupled scalar propagating in an arbitrary homogeneous, isotropic and spatially flat geometry. Our solution encompasses all previous solvable special cases such as de Sitter and power law expansion. Moreover, it can generate the mode functions for gravitons. We discuss some of the many applications that are now possible.

astro-ph↗
arXiv2003

Vacuum polarization and photon mass in inflation

We give a pedagogical review of a mechanism through which long wave length photons can become massive during inflation. Our account begins with a discussion of the period of exponentially rapid expansion known as inflation. We next describe how, when the universe is not expanding, quantum fluctuations in charged particle fields cause even empty space to behave as a polarizable medium. This is the routinely observed phenomenon of vacuum polarization. We show that the quantum fluctuations of low mass, scalar fields are enormously amplified during inflation. If one of these fields is charged, the vacuum polarization effect of flat space is strengthened to the point that long wave length photons acquire mass. Our result for this mass is shown to agree with a simple model in which the massive photon electrodynamics of Proca emerges from applying the Hartree approximation to scalar quantum electrodynamics during inflation. A huge photon mass is not measured today because the original phase of inflation ended when the universe was only a tiny fraction of a second old. However, the zero-point energy left over from the epoch of large photon mass may have persisted during the post-inflationary universe as very weak, but cosmological-scale, magnetic fields. It has been suggested that these small seed fields were amplified by a dynamo mechanism to produce the micro-Gauss magnetic fields observed in galaxies and galactic clusters.

astro-ph↗
arXiv2003

Post-Inflationary Dynamics

We argue that $Λ$-driven inflation must overshoot into an era of deflation. The deflationary period ends quickly with the creation of a hot dense thermal barrier to the forward propagation of quantum correlations from the period of inflationary particle production. Subsequent evolution is controlled by the balance between the persistence of this barrier and the growth in the 4-volume from which such correlations can be seen. This balance can lead to power law expansion.

hep-ph↗
arXiv2003

A Nonlocal Metric Formulation of MOND

We study a class of nonlocal, but causal, covariant and conserved field equations for the metric. Although nonlocal, these equations do not seem to possess extra graviton solutions in weak field perturbation theory. Indeed, the equations reduce to those of general relativity when the Ricci scalar vanishes throughout spacetime. When a static matter source is present we show how these equations can be adjusted to reproduce Milgrom's Modified Newtonian Dynamics in the weak field regime, while reducing to general relativity for strong fields. We compute the angular deflection of light in the weak field regime and demonstrate that it is the same as for general relativity, resulting in far too little lensing if no dark matter is present. We also study the field equations for a general Robertson-Walker geometry. An interesting feature of our equations is that they become conformally invariant in the MOND limit.

astro-ph↗
arXiv2002

The Axial Anomaly in D=3+1 Light-Cone QED

We consider $(3+1)$-dimensional, Dirac electrons of arbitrary mass, propagating in the presence of electric and magnetic fields which are both parallel to the $x^3$ axis. The magnetic field is constant in space and time whereas the electric field depends arbitrarily upon the light-cone time parameter $x^+ = (x^0 + x^3)/\sqrt{2}$. We present an explicit solution to the Heisenberg equations for the electron field operator in this background. The electric field results in the creation of electron-positron pairs. We compute the expectation values of the vector and axial vector currents in the presence of a state which is free vacuum at $x^+ = 0$. Both current conservation and the standard result for the axial vector anomaly are verified for the first time ever in $(3+1)$-dimensional light-cone QED. An interesting feature of our operator solution is the fact that it depends in an essential way upon operators from the characteristic at $x^- = -L$, in addition to the usual dependence upon operators at $x^+ = 0$. This dependence survives even in the limit of infinite $L$. Ignoring the $x^-$ operators leads to a progressive loss of unitarity, to the violation of current conservation, to the loss of renormalizability, and to an incorrect result for the axial vector anomaly.

hep-ph↗
arXiv2002

Super-Acceleration from Massless, Minimally Coupled $ϕ^4$

We derive a simple form for the propagator of a massless, minimally coupled scalar in a locally de Sitter geometry of arbitrary spacetime dimension. We then employ it to compute the fully renormalized stress tensor at one and two loop orders for a massless, minimally coupled phi^4 theory which is released in Bunch-Davies vacuum at t=0 in co-moving coordinates. In this system the uncertainty principle elevates the scalar above the minimum of its potential, resulting in a phase of super-acceleration. With the non-derivative self-interaction the scalar's breaking of de Sitter invariance becomes observable. It is also worth noting that the weak energy condition is violated on cosmological scales. An interesting subsidiary result is that canceling overlapping divergences in the stress tensor requires a conformal counterterm which has no effect on purely scalar diagrams.

gr-qc↗
arXiv2002

One Loop Vaccum Polarization in a Locally de Sitter Background

We compute the one loop vacuum polarization from massless, minimally coupled scalar QED in a locally de Sitter background. Gauge invariance is maintained through the use of dimensional regularization, whereas conformal invariance is explicitly broken by the scalar kinetic term as well as through the conformal anomaly. A fully renormalized result is obtained. The one loop corrections to the linearized, effective field equations do not vanish when evaluated on-shell. In fact the on-shell one loop correction depends quadratically on the inflationary scale factor, similar to a photon mass. The contribution from the conformal anomaly is insignificant by comparison.

gr-qc↗
arXiv2001

Resolving the $p^+ = 0$ Ambiguity in a Homogeneous Electric Background

I present an exact solution for the Heisenberg picture, Dirac electron in the presence of an electric field which depends arbitrarily upon the light cone time parameter $x^+ = (t+x)/\sqrt{2}$. This is the largest class of background fields for which the mode functions have ever been obtained. The solution applies to electrons of any mass and in any spacetime dimension. The traditional ambiguity at $p^+ = 0$ is explicitly resolved. It turns out that the initial value operators include not only $(I + γ^0 γ^1) ψ$ at $x^+ = 0$ but also $(I - γ^0 γ^1) ψ$ at $x^- = -L$. Pair creation is a discrete and instantaneous event on the light cone, so one can compute the particle production rate in real time. In $D=1+1$ dimensions one can also see the anomaly. Another novel feature of the solution is that the expectation value of the current operators depends nonanalytically upon the background field. This seems to suggest a new, strong phase of QED.

hep-th↗
arXiv2001

Effective Field Equations of the Quantum Gravitational Back-Reaction on Inflation

Quantum gravitational back-reaction offers the potential of simultaneously resolving the problem of the cosmological constant and providing a natural model of inflation in which scalars play no special role. In this model inflation begins because the cosmological constant is not unnaturally small. It ends through the accumulated gravitational interaction between virtual gravitons which are ripped apart by the inflationary expansion. Although perturbative techniques can be used to study the effect as long as it remains weak, they break down when back-reaction begins to exert an appreciable effect on the expansion rate. In this talk I argue that the end of inflation is sudden and that there is actually an overshoot into deflation. (This incidentally provides a very efficient mechanism for reheating.) The subsequent evolution can be understood in terms of a competition between the opening of the past light cone and the formation of a thermal barrier to the persistence of correlations from during the period of inflation.

astro-ph↗
arXiv2001

Pair creation and axial anomaly in light-cone $QED_2$

The 1+1 dimensional massive Dirac equation is solved exactly in light-cone coordinates for $x^+ > 0$ and $x^- > -L$, in the presence of an arbitrary $x^+$ dependent electric field. Our solution resolves the ambiguity at $p^+ = 0$. We also obtain the one loop rate for pair production for a positive electric field, compute the expectation values of the vector and axial vector currents, and recover the well known anomaly $e^2 E/π$ in the divergence of the latter. A final intriguing result is that the theory seems to exhibit a phase transition in the limit of infinite $L$.

hep-th↗