The averaged null energy condition (ANEC) requires that the integral over a complete null geodesic of the stress-energy tensor projected onto the geodesic tangent vector is never negative. This condition is sufficient to prove many important theorems in general relativity, but it is violated by quantum fields in curved spacetime. However there is a weaker condition, which is free of known violations, requiring only that there is no self-consistent spacetime in semiclassical gravity in which ANEC is violated on a complete, achronal null geodesic. We indicate why such a condition might be expected to hold and show that it is sufficient to rule out closed timelike curves and wormholes connecting different asymptotically flat regions.

A numerical simulation of the full bosonic sector of the $SU(2)\times U(1)$ electroweak standard model in $3+1$ dimensions demonstrates the existence of an oscillon—an extremely long-lived, localized, oscillatory solution to the equations of motion—when the Higgs mass is equal to twice the $W^{\pm }$ boson mass. The oscillon contains total energy 7 TeV localized in a region of radius 0.05 fm.

We investigate the nonlinear dynamics of hybrid inflation models, which are characterized by two real scalar fields interacting quadratically. We start by solving numerically the coupled Klein-Gordon equations in static Minkowski spacetime, searching for possible coherent structures. We find long-lived, localized configurations, which we identify as a new kind of oscillon. We demonstrate that these two-field oscillons allow for “excited” states with much longer lifetimes than those found in previous studies of single-field oscillons. We then solve the coupled field equations in an expanding Friedmann-Robertson-Walker spacetime, finding that as the field responsible for inflating the Universe rolls down to oscillate about its minimum, it triggers the formation of long-lived two-field oscillons, which can contribute up to 20% of the total energy density of the Universe. We show that these oscillons emerge for a wide range of parameters consistent with WMAP 7-year data. These objects contain total energy of about $25\times {10}^{20}\mathrm{GeV}$, localized in a region of approximate radius $6\times {10}^{-26}\mathrm{cm}$. We argue that these structures could have played a key role during the reheating of the Universe.

We study classical dynamics in the spherical ansatz for the $SU(2)$ gauge and Higgs fields of the electroweak standard model in the absence of fermions and the photon. With the Higgs boson mass equal to twice the gauge boson mass, we numerically demonstrate the existence of oscillons, extremely long-lived localized configurations that undergo regular oscillations in time. We have only seen oscillons in this reduced theory when the masses are in a two-to-one ratio. If a similar phenomenon were to persist in the full theory, it would suggest a preferred value for the Higgs mass.

We consider a ($1+1$) dimensional scalar field theory that supports oscillons, which are localized, oscillatory, stable solutions to nonlinear equations of motion. We study this theory in an expanding background and show that oscillons now lose energy, but at a rate that is exponentially small when the expansion rate is slow. We also show numerically that a universe that starts with (almost) thermal initial conditions will cool to a final state where a significant fraction of the energy of the universe—on the order of 50%—is stored in oscillons. If this phenomenon persists in realistic models, oscillons may have cosmological consequences.

We investigate the rich nonlinear dynamics during the end of hilltop inflation by numerically solving the coupled Klein-Gordon-Friedmann equations in an expanding universe. In particular, we search for coherent, nonperturbative configurations that may emerge due to the combination of nontrivial couplings between the fields and resonant effects from the cosmological expansion. We couple a massless field to the inflaton to investigate its effect on the existence and stability of coherent configurations and the effective equation of state at reheating. For parameters consistent with data from the Planck and WMAP satellites, and for a wide range of couplings between the inflaton and the massless field, we identify a transition from disorder to order characterized by emergent oscillonlike configurations. We verify that these configurations can contribute a maximum of roughly 30% of the energy density in the universe. At late times their contribution to the energy density drops to about 3%, but they remain long lived on cosmological time scales, being stable throughout our simulations. Cosmological oscillon emergence is described using a new measure of order in field theory known as relative configurational entropy.