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We present a phenomenological interaction with a scale factor power law formwhich leads to the appearance of two kinds of perturbed terms, a scale factorspatial variation along with perturbed Hubble expansion rate. We study both thebackground and the perturbation evolution within the parametrizedpost-Friedmann scheme, obtaining that the exchange of energy-momentum can flowfrom dark energy to dark matter in order to keep dark energy and dark matterdensities well defined at all times. We combine several measures of the cosmicmicrowave background (WMAP9+Planck) data, baryon acoustic oscillationmeasurements, redshift-space distortion data, JLA sample of supernovae, andHubble constant for constraining the coupling constant and the exponentprovided both parametrized the interaction itself. The joint analysis of ${\rmPlanck+WMAP9+BAO}$ ${\rm +RSD+JLA+HST}$ data seems to favor large couplingconstant, $\xi_c = 0.34403427_{- 0.18907353}^{+ 0.14430125}$ 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 CMBtemperature power spectrum indicates that a large coupling constant produces ashift 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 matterpower spectrum are sensitive to the variation of the coupling constant and the$\beta$ exponent. In this context, the interaction alters the scale of matterand radiation equality and pushes it away from the present era, which in turngenerates a shift of the turnover point toward to smaller scale.

Exploring a new interaction between dark matter and dark energy using the growth rate of structure