  It is the goal of this dissertation to demonstrate that beyond the standard
model, certain theories exist which solve conflicts between observation and
theory -- conflicts such as massive neutrinos, dark matter, unstable Higgs
vacuum, and recent Planck observations of excess relativistic degrees of
freedom in the early universe. Theories explored include a D-brane inspired
construct of U(3) X Sp(1) X U(1) X U(1) extension of the standard model, in
which we demonstrate several possible observables that may be detected at the
LHC, and an ability to stabilize the Higgs mechanism. The extended model can
also explain recent Planck data which, when added to HST data gives an excess
of relativistic degrees of freedom of \Delta N = 0.574 +- 0.25 above the
standard result. Also explored is a possible non-thermal dark matter model for
explanation of this result. Recent observations of Fermi bubble results
indicate a signal of a 50 GeV dark matter particle annihilating into b b-bar,
with a thermally averaged annihilation cross section corresponding to < \sigma
v> = 8 X 10^(-27) cm^3/s, spurs interest in a Higgs portal model suggested by
Steven Weinberg. Other implications of this model are also explored such as its
ability to explain dark matter direct detection results along with LHC Higgs
data, and Planck data. Particle physics is complimented by possible stochastic
gravitational wave searches for which a model of second order global phase
transitions is explored. These transitions generate gravitational wave spectra
with amplitudes of order \Omega_{gw} h^2 = 10^(-24) - 10^(-15). Furthermore,
techniques into such calculations are investigated in hopes to improve the
stability required in such lattice simulations.
