Self-similar cosmological solutions with a nonminimally coupled scalar field

We present self-similar cosmological solutions for a barotropic fluid plus scalar field with Brans-Dicke-type coupling to the spacetime curvature and an arbitrary power-law potential energy. We identify all the fixed points in the autonomous phase plane, including a scaling solution where the fluid density scales with the scalar field's kinetic and potential energy. This is related by a conformal transformation to a scaling solution for a scalar field with an exponential potential minimally coupled to the spacetime curvature, but nonminimally coupled to the barotropic fluid. Radiation is automatically decoupled from the scalar field, but energy transfer between the field and nonrelativistic dark matter can lead to a change to an accelerated expansion at late times in the Einstein frame. The scalar field density can mimic a cosmological constant even for steep potentials in the strong-coupling limit.