Evolution of curvature and anisotropy near a nonsingular bounce
  We consider bouncing cosmologies in which an ekpyrotic contraction phase with
w >> 1 is followed by a bouncing phase with w < -1 that violates the null
energy condition. The bouncing phase, induced by ghost condensation, is
designed to produce a classically nonsingular bounce at a finite value of the
scale factor. We show that the initial curvature and anisotropy, though diluted
during the ekpyrotic phase, grow back exponentially during the bouncing phase.
Moreover, curvature perturbations and anisotropy are generated by quantum
fluctuations during the ekpyrotic phase. In the bouncing phase, however, an
adiabatic curvature perturbation grows to dominate and contributes a blue
spectrum that spoils the scale-invariance. Meanwhile, a scalar shear
perturbation grows nonlinear and creates an overwhelming anisotropy that
disrupts the nonsingular bounce altogether.
