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.