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

Abstract

We present an impact of coupling between dark matter and a scalar field, which might be responsible for dark energy, on measurements of redshift-space distortions. We point out that, in the presence of conformal and/or disformal coupling, linearized continuity and Euler equations for total matter fluid significantly deviate from the standard ones even in the sub-horizon scales. In such a case, 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 baryon, leading to a large modification of the physical interpretation of observed data obtained by measurements of redshift-space distortions. We reformulate galaxy two-point correlation function in the redshift space based on the modified continuity and Euler equations. We conclude from the resultant formula that the true value of the linear growth rate of large-scale structure cannot be necessarily constrained by single-redshift measurements of the redshift-space distortions, unless one observes the actual time-evolution of structure.