Generating scale-invariant tensor perturbations in the non-inflationary
  universe
  It is believed that the recent detection of large tensor perturbations
strongly favors the inflation scenario in the early universe. This common sense
depends on the assumption that Einstein's general relativity is valid at the
early universe. In this paper we show that nearly scale-invariant primordial
tensor perturbations can be generated during a contracting phase before the
radiation dominated epoch if the theory of gravity is modified by the
scalar-tensor theory at that time. The scale-invariance protects the tensor
perturbations from suppressing at large scales and they may have significant
amplitudes to fit BICEP2's result. We construct a model to achieve this purpose
and show that the universe can bounce to the hot big bang after long time
contraction, and at almost the same time the theory of gravity approaches to
general relativity through stabilizing the scalar field. Theoretically, such
models are dual to inflation models if we change to the frame in which the
theory of gravity is general relativity. Dual models are related by the
conformal transformations. With this study we reinforce the point that only the
conformal invariant quantities such as the scalar and tensor perturbations are
physical. How did the background evolve before the radiation time depends on
the frame and has no physical meaning. It is impossible to distinguish
different pictures by later time cosmological probes.
