Parametric resonance of entropy perturbations in massless preheating

In this paper, we revisit the question of possible preheating of entropy modes in a two-field model with a massless inflaton coupled to a matter scalar field. Using a perturbative approximation to the covariant method we demonstrate that there is indeed a parametric instability of the entropy mode which then at second-order leads to exponential growth of the curvature fluctuation on super-Hubble scale. Back-reaction effects shut off the induced curvature fluctuations, but possibly not early enough to prevent phenomenological problems. This confirms previous results obtained using different methods and resolves a controversy in the literature.

Electroweak Radiative Corrections to Parity-Violating Asymmetry in Møller Scattering

We have computed the lowest-order electroweak radiative corrections (sans vacuum polarization contribution) to parity-violating observables in polarized Møller scattering. A covariant method of removing infrared divergences is applied, which allows to compute the corrections without introducing any unphysical parameters. When applied to the kinematics of SLAC E158 experiment, the considered radiative corrections reduce the parity-violating asymmetry by about 13%.

COVARIANT TECHNIQUES FOR COMPUTATION OF THE HEAT KERNEL

The heat kernel associated with an elliptic second-order partial differential operator of Laplace type acting on smooth sections of a vector bundle over a Riemannian manifold, is studied. A general manifestly covariant method for computation of the coefficients of the heat kernel asymptotic expansion is developed. The technique enables one to compute explicitly the diagonal values of the heat kernel coefficients, so called Hadamard–Minakshisundaram–De Witt–Seeley coefficients, as well as their derivatives. The elaborated technique is applicable for a manifold of arbitrary dimension and for a generic Riemannian metric of arbitrary signature. It is very algorithmic, and well suited to automated computation. The fourth heat kernel coefficient is computed explicitly for the first time. The general structure of the heat kernel coefficients is investigated in detail. On the one hand, the leading derivative terms in all heat kernel coefficients are computed. On the other hand, the generating functions in closed covariant form for the covariantly constant terms and some low-derivative terms in the heat kernel coefficients are constructed by means of purely algebraic methods. This gives, in particular, the whole sequence of heat kernel coefficients for an arbitrary locally symmetric space.

A LIE GROUP FRAMEWORK FOR COMPOSITE PARTICLES AND HARMONIC OSCILLATOR MASS SPECTRUM

A harmonic oscillator mass spectrum is developed through a relativistic covariant method in unifying the external and internal variables of a hadron leading to a dynamical Lie algebra. It is shown that through the introduction of an internal variable ξμ, which behaves as a 'direction vector', attached to each space-time point, χμ, and the spatial extension, Xi, of the composite system, we can uniquely determine a harmonic oscillator mass spectrum. This is valid even when the constituents are taken to be massless. Moreover, when these internal variables are associated with the internal symmetry, the mass splitting due to the internal symmetry breaking is incorporated in this formalism and no adhoc consideration is necessary. The mass spectrum of the neutral isovector and isoscalar mesons is computed in this framework.