Analytic and numerical techniques are presented for computing gravitational production of scalar particles in the limit that the inflaton mass is much larger than the Hubble expansion rate at the end of inflation. These techniques rely upon adiabatic invariants and time modeling of a typical inflaton field which has slow and fast time variation components. A faster computation time for numerical integration is achieved via subtraction of slowly varying components that are ultimately exponentially suppressed. The fast oscillatory remnant results in production of scalar particles with a mass larger than the inflationary Hubble expansion rate through a mechanism analogous to perturbative particle scattering. An improved effective Boltzmann collision equation description of this particle production mechanism is developed. This model allows computation of the spectrum using only adiabatic invariants, avoiding the need to explicitly solve the inflaton equations of motion.

Previous numerical investigations of gravitational particle production during the coherent oscillation period of inflation displayed unexplained fluctuations in the spectral density of the produced particles. We argue that these features are due to the quantum interference of the coherent scattering reactions that produce the particles. We provide accurate analytic formulae to compute the particle production amplitude for a conformally- coupled scalar field, including the interference effect in the kinematic region where the production can be interpreted as inflaton scattering into scalar final states via graviton exchange.

Deep inelastic scattering of very high-energy neutrinos can potentially be enhanced by the production of a single top quark or charm quark via the interaction of a virtual W -boson exchange with a b-quark or s-quark parton in the nucleon. The single top contribution shows a sharp rise at neutrino energies above 0.5 PeV and gives a cross-section contribution of order 5 percent at 10 PeV, while single charm has a low energy threshold and contributes about 25 percent. Semileptonic decays of top and charm give dimuon events whose kinematic characteristics are shown. The angular separation of the dimuons from heavy quark production in the IceCube detector can reach up to one degree. Top quark production has a unique, but rare, three muon signal.

Basis tensor gauge theory is a vierbein analog reformulation of ordinary gauge theories in which the difference of local field degrees of freedom has the interpretation of an object similar to a Wilson line. Here we present a non-Abelian basis tensor gauge theory formalism. Unlike in the Abelian case, the map between the ordinary gauge field and the basis tensor gauge field is nonlinear. To test the formalism, we compute the beta function and the two-point function at the one-loop level in non-Abelian basis tensor gauge theory and show that it reproduces the well-known results from the usual formulation of non-Abelian gauge theory.

Basis tensor gauge theory (BTGT) is a vierbein analog reformulation of ordinary gauge theories in which the vierbein field describes the Wilson line. After a brief review of the BTGT, we clarify the Lorentz group representation properties associated with the variables used for its quantization. In particular, we show that starting from an SO(1,3) representation satisfying the Lorentz-invariant U(1,3) matrix constraints, BTGT introduces a Lorentz frame choice to pick the Abelian group manifold generated by the Cartan subalgebra of U(1,3) for the convenience of quantization even though the theory is frame independent. This freedom to choose a frame can be viewed as an additional symmetry of BTGT that was not emphasized before. We then show how an [Formula: see text] permutation symmetry and a parity symmetry of frame fields natural in BTGT can be used to construct renormalizable gauge theories that introduce frame-dependent fields but remain frame independent perturbatively without any explicit reference to the usual gauge field.