Are redshift-space distortions actually a probe of growth of structure?

Abstract

Although multiple cosmological observations indicate the existence of dark matter and dark energy, cosmological tests of interactions between them have not yet been established. We point out that, in the presence of a coupling between dark matter and dark energy, a peculiar velocity of total matter field is determined not only by a logarithmic time-derivative of its density perturbation but also by density perturbations for both dark matter and baryonic matter, leading to a large modification of the physical interpretation of observed data obtained by measurements of redshift-space distortions. We reformulate a galaxy two-point correlation function in the redshift space based on the modified continuity and Euler equations. We conclude from the resultant formula that redshift space distortions provide us information on the coupling between dark matter and the scalar field by combining weak lensing measurements.