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 { Planck + WMAP 9 + BAO } { + RSD + JLA + HST } data seems to favor large interacting coupling , \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 .