We perform a complete next-to-leading order calculation of the non-Abelian electric field correlator in a SU(Nc) plasma, which encodes properties of the plasma relevant for heavy particle bound state formation and dissociation, and is different from the correlator for the heavy quark diffusion coefficient. The calculation is carried out in the real-time formalism of thermal field theory and includes both vacuum and finite temperature contributions. By working in the Rξ gauge, we explicitly show the results are gauge independent, infrared and collinear safe. The renormalization group equation of this electric field correlator is determined by that of the strong coupling constant. Our next-to-leading order calculation can be directly applied to any dipole singlet-adjoint transition of heavy particle pairs. For example, it can be used to describe dissociation and (re)generation of heavy quarkonia inside the quark-gluon plasma well below the melting temperature, as well as heavy dark matter pairs (or charged co-annihilating partners) in the early universe.

In this paper, we show how the structure of the landscape potential of the primordial Universe may be probed through the properties of the primordial density perturbations responsible for the origin of the cosmic microwave background anisotropies and the large-scale structure of our Universe. Isocurvature fields -fields orthogonal to the inflationary trajectory-may have fluctuated across the barriers separating local minima of the landscape potential during inflation. We analyze how this process could have impacted the evolution of the primordial curvature perturbations. If the typical distance separating consecutive minima of the landscape potential and the height of the potential barriers are smaller than the Hubble expansion rate parametrizing inflation, the probability distribution function of isocurvature fields becomes non-Gaussian due to the appearance of bumps and dips associated with the structure of the potential. We show that this non-Gaussianity can be transferred to the statistics of primordial curvature perturbations if the isocurvature fields are coupled to the curvature perturbations. The type of non-Gaussian structure that emerges in the distribution of curvature perturbations cannot be fully probed with the standard methods of polyspectra; instead, the probability distribution function is needed. The latter is obtained by summing all the n-point correlation functions. To substantiate our claims, we offer a concrete model consisting of an axionlike isocurvature perturbation with a sinusoidal potential and a linear derivative coupling between the isocurvature and curvature field. In this model, the probability distribution function of the curvature perturbations consists of a Gaussian function with small superimposed oscillations reflecting the isocurvature axion potential.

We show that the shape of the inflationary landscape potential may be constrained by analyzing cosmological data. The quantum fluctuations of fields orthogonal to the inflationary trajectory may have probed the structure of the local landscape potential, inducing non-Gaussianity (NG) in the primordial distribution of the curvature perturbations responsible for the cosmic microwave background (CMB) anisotropies and our Universe's large-scale structure. The resulting type of NG (tomographic NG) is determined by the shape of the landscape potential, and it cannot be fully characterized by 3-or 4-point correlation functions. Here we deduce an expression for the profile of this probability distribution function in terms of the landscape potential, and we show how this can be inverted in order to reconstruct the potential with the help of CMB observations. While current observations do not allow us to infer a significant level of tomographic NG, future surveys may improve the possibility of constraining this class of primordial signatures.Is there any feature about our Universe that would require us to assume primordial non-Gaussian initial conditions? Up until now, cosmic microwave background (CMB) and large-scale structure (LSS) observations are fully consistent with the premise that the primordial curvature perturbations were initially distributed according to a perfectly Gaussian statistics [1,2]. This has favored the simplest models of inflation -single field slowroll inflation-based on the steady evolution of a scalar field driven by a flat potential [3][4][5][6][7]. In these models, the self-interactions of the primordial curvature perturbation lead to tiny non-Gaussianities suppressed by the slow-roll parameters characterizing the evolution of the Hubble expansion rate H, during inflation [8][9][10][11].The confirmation of non-Gaussian initial conditions would help us to decipher certain fundamental aspects about inflation [12][13][14][15]. Indeed, non-Gaussianity (NG) can be generated by nonlinearities affecting the evolution of primordial curvature perturbations (denoted as ζ). These nonlinearities are the result of self-interactions, or interactions with other degrees of freedom, such as isocurvature fields (fields orthogonal to the inflationary trajectory in multifield space). Inevitably, perturbation theory limits the extent to which we can study the emergence of NG, forcing us to focus on the lowest order operators (in terms of field powers) in the ζ Lagrangian. Thus, most of the recent effort devoted to the study of NG has relied on parametrizing it with the bispectrum and trispectrum, the amplitudes of the 3-and 4-point correlation functions of ζ in momentum space. Understanding how different interactions lead to different shapes and runnings of the bispectrum has constituted one of the main programs in the study of inflation [12][13][14][15].It is conceivable, however, that certain classes of interactions may lead to NG deviations that cannot be parametrized just with the bispectrum and/or trispectrum....

A canonical quantization procedure is applied to elastic waves interacting with pinned dislocation segments ("strings") of length L via the Peach-Koehler force. The interaction Hamiltonian, derived from an action principle that classically generates the Peach-Koehler force, is a power series of creation and annihilation operators. The leading term is quadratic, and keeping only this term the observable quantities of scattering processes are computed to all orders in perturbation theory. The resulting theory is characterized by the magnitude of kL, with k the wavenumber of an incident phonon. The theory is solved for arbitrary kL, and different limits are explored. A significant result at this level is the scattering cross section for phonons by dislocation segments. As a function of frequency, this cross section has a much richer structure than the linear-in-frequency behavior that is inferred from scattering by an infinite, static, dislocation. The rate of spontaneous phonon emission by an excited dislocation is computed as well. When many dislocations are present, an effective mass operator is computed in the Weak and Independent Scattering Approximation. The contribution of the cubic terms is computed to leading order in perturbation theory. They allow for a comparison of the scattering of a phonon by a string and the three-phonon scattering, as well as studying the dependence of scattering amplitudes on the temperature of the solid. It is concluded that the effect of dislocations will dominate for relatively modest dislocation densities. Finally, the full power series of the interaction Hamiltonian is considered. The effects of quantum corrections, i.e., contributions proportional to Planck's constant, are estimated, and found to be controlled by another wavenumber-dependent parameter kdq, where dq is a length proportional to √ . The possibility of using the results of this paper in the study of the phononic thermal properties of two-and three-dimensional materials is noted and discussed.

Cosmic inflation may have led to non-Gaussian initial conditions that cannot be fully parametrised by 3-and/or 4-point functions. In this work, we discuss various strategies to search for primordial non-Gaussianity beyond polyspectra with the help of cosmological data. Our starting point is a generalised local ansatz for the primordial curvature perturbation ζ of the form ζ = ζ G + F NG (ζ G ), where ζ G is a Gaussian random field and F NG is an arbitrary function parametrising non-Gaussianity that, in principle, could be reconstructed from data. Noteworthily, in the case of multi-field inflation, the function F NG can be shown to be determined by the shape of tomographic sections of the landscape potential responsible for driving inflation. We discuss how this generalised local ansatz leads to a probability distribution functional that may be used to extract information about inflation from current and future observations. In particular, we derive various classes of probability distribution functions suitable for the statistical analysis of the cosmic microwave background and largescale structure.