Primordial Gravitational Waves Spectrum in the Coupled-Scalar-Tachyon
  Bounce Universe
  We derive in detail the equations of motion for the tensorial modes of
primordial metric perturbations in the Coupled-Scalar-Tachyon Bounce Universe.
We solve for the gravitational wave equations in the pre-bounce contraction and
the post-bounce expansion epochs. To match the solutions of the tensor
perturbations, we idealise the bounce process yet retaining the essential
physical properties of the bounce universe. We put forward two matching
conditions: one ensures the continuity of the gravitational wave functions and
the other respects the symmetric nature of the bounce dynamics. The matching
conditions connect the two independent modes of gravitational waves solutions
before and after the bounce. We further analyse the scale dependence and time
dependence of the gravitational waves spectra in the bounce universe and
compare them with the primordial spectrum in the single field inflation
scenario. We discuss the implications to early universe physics and present
model independent observational signatures extracted from the bounce universe.
