Exploring a new interaction between dark matter and dark energy using
  the growth rate of structure
  We present a phenomenological interaction with a scale factor power law form
which leads to the appearance of two kinds of perturbed terms, a scale factor
spatial variation along with perturbed Hubble expansion rate. We study both the
background and the perturbation evolution within the parametrized
post-Friedmann scheme, obtaining that the exchange of energy-momentum can flow
from dark energy to dark matter in order to keep dark energy and dark matter
densities well defined at all times. We combine several measures of the cosmic
microwave background (WMAP9+Planck) data, baryon acoustic oscillation
measurements, redshift-space distortion data, JLA sample of supernovae, and
Hubble constant for constraining the coupling constant and the exponent
provided both parametrized the interaction itself. The joint analysis of ${\rm
Planck+WMAP9+BAO}$ ${\rm +RSD+JLA+HST}$ data seems to favor large coupling
constant, $\xi_c = 0.34403427_{- 0.18907353}^{+ 0.14430125}$ at 1 $\sigma$
level, and prefers a power law interaction with a negative exponent, thus
$\beta= -0.50863232_{- 0.40923857}^{+ 0.48424166}$ at 1 $\sigma$ level. The CMB
temperature power spectrum indicates that a large coupling constant produces a
shift of the acoustic peaks and affects their amplitudes at lower multipoles.
In addition, a larger $\beta$ exponent generates a shift of the acoustic peaks,
pointing a clear deviation with respect to the concordance model. The matter
power spectrum are sensitive to the variation of the coupling constant and the
$\beta$ exponent. In this context, the interaction alters the scale of matter
and radiation equality and pushes it away from the present era, which in turn
generates a shift of the turnover point toward to smaller scale.
