Fluctuations for Galaxy Formation from Inflation Models.
Abstract
The theory of fluctuations for galaxy formation from chaotic inflation models is extended to include the effects of (1) multiple scalar fields, (2) curvature coupling of scalar fields to gravity, (3) nonlinear evolution of long wavelength metric and scalar fields, and (4) stochastic generation of initial conditions. Multiple scalar field models may generate more large scale power than the standard Cold Dark Matter (CDM) model if the Universe undergoes two inflation epochs giving a CDM+ plateau spectrum. If the scalar fields pass over a mogul in the potential, then CDM+ mountain fluctuation spectra may be generated. The chaotic inflation scenario may be housed within a grand unified theory (GUT) framework through a coupling of scalar Higgs field to curvature, xi Rphi ^2/2. If the curvature coupling is chosen large and negative, xi~ 2 times 10^4, then a more natural value of scalar field selfcoupling lambda ~ 0.05 gives the observed level of fluctuations. Radiative corrections to the Higgs potential are small and the reheat temperature is typically high yielding successful baryogenesis. Using HamiltonJacobi theory, a general formalism is presented for following the nonlinear evolution of the metric (scalar, vector, and tensor modes) and scalar fields for fluctuations with wavelengths greater than the Hubble radius. Employing an expansion accurate to first order in spatial gradients, the classical momentum constraint of the ArnowittDeser Misner (ADM) formalism may be integrated exactly without recourse to linear perturbation theory. It is shown how nonlinear effects of the metric and scalar fields may be included in Starobinski's formulation of stochastic inflation. Stochastic noise terms in the long wavelength evolution equations model quantum fluctuations that are assumed to become classical at horizon crossing and which then contribute to the background. T = ln(Ha) proves to be a useful time variable because it enables one to solve for scalar field quantum fluctuations within the horizon in an inhomogeneous background. A FokkerPlanck equation is formulated which describes how the probability function evolves in time. Analytic Green's function solutions are obtained for a single scalar field selfinteracting through an exponential potential.
 Publication:

Ph.D. Thesis
 Pub Date:
 1989
 Bibcode:
 1989PhDT.......155S
 Keywords:

 Physics: Elementary Particles and High Energy