Reconstruction of a Nonminimal Coupling Theory with Scale-invariant
  Power Spectrum
  A nonminimal coupling single scalar field theory, when transformed from
Jordan frame to Einstein frame, can act like a minimal coupling one. Making use
of this property, we investigate how a nonminimal coupling theory with
scale-invariant power spectrum could be reconstructed from its minimal coupling
counterpart, which can be applied in the early universe. Thanks to the coupling
to gravity, the equation of state of our universe for a scale-invariant power
spectrum can be relaxed, and the relation between the parameters in the action
can be obtained. This approach also provides a means to address the Big-Bang
puzzles and anisotropy problem in the nonminimal coupling model within Jordan
frame. Due to the equivalence between the two frames, one may be able to find
models that are free of the horizon, flatness, singularity as well as
anisotropy problems.
