Towards a Nonsingular Bouncing Cosmology
  We present a nonsingular bouncing cosmology using single scalar field matter
with non-trivial potential and non-standard kinetic term. The potential sources
a dynamical attractor solution with Ekpyrotic contraction which washes out
small amplitude anisotropies. At high energy densities the field evolves into a
ghost condensate, leading to a nonsingular bounce. Following the bounce there
is a smooth transition to standard expanding radiation and matter dominated
phases. Using linear cosmological perturbation theory we track each Fourier
mode of the curvature fluctuation throughout the entire cosmic evolution. Using
standard matching conditions for nonsingular bouncing cosmologies we verify
that the spectral index does not change during the bounce. We show there is a
controlled period of exponential growth of the fluctuation amplitude for the
perturbations (but not for gravitational waves) around the bounce point which
does not invalidate the perturbative treatment. This growth induces a natural
suppression mechanism for the tensor to scalar ratio of fluctuations. Moreover,
we study the generation of the primordial power spectrum of curvature
fluctuations for various types of initial conditions. For the pure vacuum
initial condition, on scales which exit the Hubble radius in the phase of
Ekpyrotic contraction, the spectrum is deeply blue. For thermal particle
initial condition, one possibility for generating a scale-invariant spectrum
makes use of a special value of the background equation of state during the
contracting Ekpyrotic phase. If the Ekpyrotic phase is preceded by a period of
matter-dominated contraction, the primordial power spectrum is nearly
scale-invariant on large scales (scales which exit the Hubble radius in the
matter-dominated phase) but acquires a large blue tilt on small scales.
