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We introduce a second-order stochastic effective theory for light scalar fields in de Sitter spacetime, extending the validity of the stochastic approach beyond the massless limit and demonstrating how it can be used to compute long-distance correlation functions non-perturbatively. The parameters of the second-order stochastic theory are determined from quantum field theory through a perturbative calculation, which is valid if the self-interaction parameter $\lambda$ satisfies $\lambda\ll m^2/H^2$, where $m$ is the scalar and $H$ is the Hubble rate. Therefore it allows stronger self-interactions than conventional perturbation theory, which is limited to $\lambda\ll m^4/H^4$ by infrared divergences. We demonstrate the applicability of the second-order stochastic theory by comparing its results with perturbative quantum field theory and overdamped stochastic calculations, and discuss the prospects of improving its accuracy with a full one-loop calculation of its parameters., Comment: 44 pages, 6 figures. Accepted for publication in Physical Review D

We present the results of an explicit numerical computation of a novel instanton in Georgi-Glashow SU(2) theory. The instanton is physically relevant as a mediator of Schwinger production of 't Hooft-Polyakov magnetic monopoles from strong magnetic fields. In weak fields, the pair production rate has previously been computed using the worldline approximation, which breaks down in strong fields due to the effects of finite monopole size. Using lattice field theory we have overcome this limit, including finite monopole size effects to all orders. We demonstrate that a full consideration of the internal monopole structure results in an enhancement to the pair production rate, and confirm earlier results that monopole production becomes classical at the Ambjorn-Olesen critical field strength., 9 pages, 4 figures; corrected sign error in Eq. (2)

We study the contribution to the primordial curvature perturbation on observational scales generated by the reheating field in massless preheating. To do so we use lattice simulations and a recent extension to the $\delta N$ formalism. The work demonstrates the functionality of these techniques for calculating the observational signatures of models in which non-perturbative reheating involves a light scalar field., Comment: 7 pages, 3 figures

We revisit the question of how to calculate correlations of the curvature perturbation, $\ensuremath{\zeta}$, using the $\ensuremath{\delta}N$ formalism when one cannot employ a truncated Taylor expansion of $N$. This problem arises when one uses lattice simulations to probe the effects of isocurvature modes on models of reheating. Working in real space, we use an expansion in the cross-correlation between fields at different positions and present simple expressions for observables such as the power spectrum and the reduced bispectrum, ${f}_{\mathrm{NL}}$. These take the same form as those of the usual $\ensuremath{\delta}N$ expressions, but with the derivatives of $N$ replaced by nonperturbative $\ensuremath{\delta}N$ coefficients. We test the validity of this expansion and, when compared to others in the literature, argue that our expressions are particularly well suited for use with simulations.

Light scalar fields present during inflation can lead to interesting observable signatures, especially in models with non-equilibrium reheating dynamics. We study a supersymmetric hybrid inflation model with a third scalar whose lightness is protected by symmetry, using analytical and numerical techniques, and demonstrate that the amplitude, the spectral index and the non-Gaussianity parameter fNL of the primordial curvature perturbation are within the Planck observational bounds for suitable parameter values., Comment: 8 pages, 7 figures, v2: updated to journal version

We investigate the anisotropies in the gravitational wave (GW) background produced at preheating after inflation. Using lattice field theory simulations of a massless preheating model, we show that the GW amplitude depends sensitively on the value of the decay product field chi coupled to the inflaton phi, with the only requisite that chi is light during inflation. We find a strong anisotropy in the amplitude of the GW background on large angular scales, the details of which strongly depend on the reheating dynamics. We expect similar conclusions for a wide class of inflationary models with light scalar fields. If future direct detection GW experiments are capable of detecting the GW produced by preheating, they should also be able to detect this effect. This could eventually provide a powerful way to distinguish between different inflationary and preheating scenarios., 5 pages, 3 figures

In the Yang-Mills theory, the apparent thickness of the confining string is known to grow logarithmically when its length increases. The same logarithmic broadening also happens to strings in other quantum field theories and domain walls in statistical physics models. Even in quantum field theories, the correlators used to measure and characterise this phenomenon are analogous to those in statistical physics. In this paper we describe it using the string form factor which is a meaningful quantum observable, obtainable in principle from scattering experiments. We show how the form factor can be obtained from field correlation functions calculated in lattice Monte Carlo simulations. We apply this method to 2+1-dimensional scalar theory in the strong coupling limit, where it is equivalent to the 3D Ising model, and through duality also to 2+1-dimensional $\mathbb{Z}_2$ gauge theory. We measure the string form factor by simulating the Ising model, and demonstrate that it displays the same logarithmic broadening as observed by other quantities., 10 pages, 7 figures, v2: minor changes to wording of abstract and main text, version accepted by PRD

The mass and interactions of a quantum 't Hooft-Polyakov monopole are measured nonperturbatively using correlation functions in lattice Monte Carlo simulations. A method of measuring the form factors for interactions between the monopole and fundamental particles, such as the photon, is demonstrated. These quantities are potentially of experimental relevance in searches for magnetic monopoles., 11 pages, 6 figures; v2: minor changes to introduction and conclusions, published in PRD

The form factor provides a convenient way to describe properties of topological solitons in the full quantum theory, when semiclassical concepts are not applicable. It is demonstrated that the form factor can be calculated numerically using lattice Monte Carlo simulations. The approach is very general and can be applied to essentially any type of soliton. The technique is illustrated by calculating the kink form factor near the critical point in 1+1-dimensional scalar field theory. As expected from universality arguments, the result agrees with the exactly calculable scaling form factor of the two-dimensional Ising model., 5 pages, 3 figures; v2: discussion extended, references added, version accepted for publication in PRD

We investigate twisted C-periodic boundary conditions in SU(N) gauge field theory with an adjoint Higgs field. We show that with a suitable twist for even N one can impose a nonzero magnetic charge relative to residual U(1) gauge groups in the broken phase, thereby creating a 't Hooft-Polyakov magnetic monopole. This makes it possible to use lattice Monte Carlo simulations to study the properties of these monopoles in the quantum theory.

We argue that cosmic strings with high winding numbers generally form in first-order gauge symmetry breaking phase transitions, and we demonstrate this using computer simulations. These strings are heavier than single-winding strings and therefore more easily observable. Their cosmological evolution may also be very different., 4 pages, updated to match the published version

We present a detailed numerical study of the equilibrium and non-equilibrium dynamics of the phase transition in the finite-temperature Abelian Higgs model. Our simulations use classical equations of motion both with and without hard-thermal-loop corrections, which take into account the leading quantum effects. From the equilibrium real-time correlators, we determine the Landau damping rate, the plasmon frequency and the plasmon damping rate. We also find that, close to the phase transition, the static magnetic field correlator shows power-law magnetic screening at long distances. The information about the damping rates allows us to derive a quantitative prediction for the number density of topological defects formed in a phase transition. We test this prediction in a non-equilibrium simulation and show that the relevant time scale for defect formation is given by the Landau damping rate., 22 pages, 3 figures

We consider the construction of inverted hybrid inflation models in which the vacuum energy during inflation is at the TeV scale, and the inflaton couples to the Higgs field. Such models are of interest in the context of some recently proposed models of electroweak baryogenesis. We demonstrate how constraints on these models arise from quantum corrections, and how self-consistent examples may be constructed, albeit at the expense of fine-tuning. We discuss two possible ways in which the baryon asymmetry of the universe may be produced in these models. One of them is based on preheating and a consequent non-thermal electroweak symmetry restoration and the other on the formation of Higgs winding configurations by the Kibble mechanism at the end of inflation., Comment: 21 pages, 5 figures. Minor changes, some references added. To appear in PRD

The time evolution of soft modes in a quantum gauge field theory is to first approximation classical, but the equations of motion are non-local. We show how they can be written in a local and Hamiltonian way in an Abelian theory, and that this formulation is particularly suitable for numerical simulations. This makes it possible to simulate numerically non-equilibrium processes such as the phase transition in the Abelian Higgs model and and to study, for instance, bubble nucleation and defect formation. Such simulations would also help to understand phase transitions in more complicated gauge theories. Moreover, we show that the existing analytical results for the time-evolution in a pure-gauge theory correspond to a special class of initial conditions and that different initial conditions can lead to qualitatively different behavior. We compare the results of the simulations to analytical calculations and find an excellent agreement., Comment: 18 pages, 5 figures, REVTeX

QCD matter, a spatially and temporally extended sys- tem of matter described by the laws of Quantum Chro- modynamics, goes at high temperatures into a quark- gluon plasma phase, in which color is no more confined and chiral symmetry is restored. An essential quantity, describing coherent static interactions in the plasma, is the inverse screening length of color electric fields, the Debye mass mD. The Debye mass enters in many essen- tial characteristics of static properties of the plasma. Its numerical value is important for phenomenological dis- cussions of formation of the quark-gluon plasma, for the analysis of J/� andsuppression in heavy ion colli- sions, for the computation of parton equilibration rates, etc. (see, e.g. (1)). The definition and computation of the Debye mass for abelian QED plasma is well understood (2). The electro- magnetic current jµ is a gauge-invariant quantity, and the Debye mass can be extracted from the 2-point gauge invariant correlation function of j0 in the plasma. There are no massless charged particles in QED, which allows an infrared-safe perturbative computation of the Debye mass in powers of the electromagnetic coupling e. This has been done to order e 5 (3). The situation in QCD is much more complicated. First, the corresponding cur- rent in QCD, j a , is not a gauge invariant quantity. Sec- ond, there are massless charged gluons which give rise to infrared divergences and prevent the perturbative deter- mination of the Debye mass beyond leading order. A non-perturbative gauge invariant definition of the Debye mass in vectorlike theories with zero chemical po- tential was suggested in (4). According to it, mD can be defined from the large distance exponential fall-off of correlators of gauge-invariant time-reflection odd opera- tors O, h O(τ, ~ x)O(τ,0)i ∼ C|~