  We study the predictions for structure formation in an induced gravity dark
energy model with a quartic potential. By developing a dedicated
Einstein-Boltzmann code, we study self-consistently the dynamics of homogeneous
cosmology and of linear perturbations without using any parametrization. By
evolving linear perturbations with initial conditions in the radiation era, we
accurately recover the quasi-static analytic approximation in the matter
dominated era. We use Planck 2013 data and a compilation of baryonic acoustic
oscillation (BAO) data to constrain the coupling $\gamma$ to the Ricci
curvature and the other cosmological parameters. By connecting the
gravitational constant in the Einstein equation to the one measured in a
Cavendish-like experiment, we find $\gamma < 0.0012$ at 95% CL with Planck 2013
and BAO data. This is the tightest cosmological constraint on $\gamma$ and on
the corresponding derived post-Newtonian parameters. Because of a degeneracy
between $\gamma$ and the Hubble constant $H_0$, we show how larger values for
$\gamma$ are allowed, but not preferred at a significant statistical level,
when local measurements of $H_0$ are combined in the analysis with Planck 2013
data.
