The dynamical viability of scalar-tensor gravity theories

We establish the dynamical attractor behavior in scalar-tensor theories of dark energy, providing a powerful framework to analyze classes of theories, predicting common evolutionary characteristics that can be compared against cosmological constraints. In the Jordan frame the theories are viewed as a coupling between a scalar field, Phi, and the Ricci scalar, R, F(Phi) R. The Jordan frame evolution is described in terms of dynamical variables m equivalent to d ln F/d ln Phi and r equivalent to -Phi F/f, where F(Phi) = df (Phi)/d Phi. The evolution can be alternatively viewed in the Einstein frame as a general coupling between scalar dark energy and matter, beta. We present a complete, consistent picture of evolution in the Einstein and Jordan frames and consider the conditions on the form of the coupling F and beta required to give the observed cold dark matter (CDM) dominated era that transitions into a late-time accelerative phase, including transitory accelerative eras that have not previously been investigated. We find five classes of evolutionary behavior of which four are qualitatively similar to those for f (R) theories (which have beta = 1/2). The fifth class exists only for |beta| < root 3/4, i.e. not for f (R) theories. In models giving transitory late-time acceleration, we find a viable accelerative region of the (r, m) plane accessible to scalar-tensor theories with any coupling, beta (at least in the range |beta| <= 1/2, which we study in detail), and an additional region open only to theories with |beta| < root 3/4.