Nearly scale-invariant power spectrum and quantum cosmological
  perturbations in the gravity's rainbow scenario
  We propose the gravity's rainbow scenario as a possible alternative of the
inflation paradigm to account for the flatness and horizon problems. We focus
on studying the cosmological scalar perturbations which are seeded by the
quantum fluctuations in the very early universe. The scalar power spectrum is
expected to be nearly scale-invariant. We estimate the rainbow index $\lambda$
and energy scale $M$ in the gravity's rainbow scenario by analyzing the Planck
temperature and WMAP polarization datasets. The constraints on them are given
by $\lambda=2.933\pm0.012$ and $\ln (10^5M/M_p)= -0.401^{+0.457}_{-0.451}$ at
the $68\%$ confidence level.
