  The expansion history of the Universe reconstructed from a combination of
recent data indicates a preference for a changing Dark Energy (DE) density.
Moreover, the DE density appears to be increasing with cosmic time, with its
equation of state being below -1 on average, and possibly crossing the
so-called phantom divide. Scalar-tensor theories, in which the scalar field
mediates a force between matter particles, offer a natural framework in which
the effective DE equation of state can be less than -1 and cross the phantom
barrier. We consider the generalized Brans-Dicke (GBD) class of scalar-tensor
theories and reconstruct their Lagrangian given the effective DE density
extracted from recent data. Then, given the reconstructed Lagrangian, we solve
for the linear perturbations and investigate the characteristic signatures of
these reconstructed GBD in the cosmological observables, such as the cosmic
microwave background (CMB) anisotropy, the galaxy number counts, and their
cross-correlations. In particular, we demonstrate that the Integrated
Sachs-Wolfe (ISW) effect probed by the cross-correlation of CMB with the matter
distribution can rule out scalar-tensor theories as the explanation of the
observed DE dynamics independently from the laboratory and solar system fifth
force constraints.
