CMB Fluctuation Amplitude from Dark Energy Partitions

It is assumed that the dark energy observed today is frozen as a result of a phase transition involving the source of that energy. Postulating that the dark energy de-coherence which results from this phase transition drives statistical variations in the energy density specifies a class of cosmological models in which the cosmic microwave background (CMB) fluctuation amplitude at last scattering is approximately $10^{-5}$.Comment: 7 Pages, Poster presented at Texas@Stanford conference, Dec. 2004, minor clarification

A Non-Perturbative, Finite Particle Number Approach to Relativistic Scattering Theory

We present integral equations for the scattering amplitudes of three scalar particles, using the Faddeev channel decomposition, which can be readily extended to any finite number of particles of any helicity. The solution of these equations, which have been demonstrated to be calculable, provide a non-perturbative way of obtaining relativistic scattering amplitudes for any finite number of particles that are Lorentz invariant, unitary, cluster decomposable and reduce unambiguously in the non-relativistic limit to the non-relativistic Faddeev equations. The aim of this program is to develop equations which explicitly depend upon physically observable input variables, and do not require renormalization or dressing of these parameters to connect them to the boundary states

Evidence for a Cosmological Phase Transition on the TeV Scale

Examining the reverse evolution of the universe from the present, long before reaching Planck density dynamics one expects major modifications from the de-coherent thermal equations of state, suggesting a prior phase that has macroscopic coherence properties. The assumption that the phase transition occurs during the radiation dominated epoch, and that zero-point motions drive the fluctuations associated with this transition, specifies a class of cosmological models in which the cosmic microwave background fluctuation amplitude at last scattering is approximately $10^{-5}$. Quantum measurability constraints (eg. uncertainly relations) define cosmological scales whose expansion rates can be at most luminal. Examination of these constraints for the observed dark energy density establishes a time interval from the transition to the present. It is shown that the dark energy can consistently be interpreted as due to the vacuum energy of collective gravitational modes which manifest as the zero-point motions of coherent Planck scale mass units prior to the gravitational quantum de-coherence of the cosmology. A scenario is suggested that connects microscopic physics to the relevant cosmological scale.Comment: 35 page

Construction of Non-Perturbative, Unitary Particle-Antiparticle Amplitudes for Finite Particle Number Scattering Formalisms

Starting from a unitary, Lorentz invariant two-particle scattering amplitude , we show how to use an identification and replacement process to construct a unique, unitary particle-antiparticle amplitude. This process differs from conventional on-shell Mandelstam s,t,u crossing in that the input and constructed amplitudes can be off-diagonal and off-energy shell. Further, amplitudes are constructed using the invariant parameters which are appropriate to use as driving terms in the multi-particle, multichannel non-perturbative, cluster decomposable, relativistic scattering equations of the Faddeev-type integral equations recently presented by Alfred, Kwizera, Lindesay and Noyes. It is therefore anticipated that when so employed, the resulting multi-channel solutions will also be unitary. The process preserves the usual particle-antiparticle symmetries. To illustrate this process, we construct a J=0 scattering length model chosen for simplicity. We also exhibit a class of physical models which contain a finite quantum mass parameter and are Lorentz invariant. These are constructed to reduce in the appropriate limits, and with the proper choice of value and sign of the interaction parameter, to the asymptotic solution of the non-relativistic Coulomb problem, including the forward scattering singularity, the essential singularity in the phase, and the Bohr bound-state spectrum