Modified Gravity and the CMB
  We consider the effect of modified gravity on the peak structure of the
Cosmic Microwave Background (CMB) spectrum. We focus on simple models of
modified gravity mediated by a massive scalar field coupled to both baryons and
cold dark matter. This captures the features of chameleon, symmetron, dilaton
and $f(R)$ models. We find that the CMB peaks can be affected in three
independent ways provided the Compton radius of the massive scalar is not
far-off the sound horizon at last scattering. When the coupling of the massive
scalar to Cold Dark Matter (CDM) is large, the anomalous growth of the CDM
perturbation inside the Compton radius induces a change in the peak amplitudes.
When the coupling to baryons is moderately large, the speed of sound is
modified and the peaks shifted to higher momenta. Finally when both couplings
are non-vanishing, a new contribution proportional to the Newton potential
appears in the Sachs-Wolfe temperature and increases the peak amplitudes. We
also show how, given any temporal evolution of the scalar field mass, one can
engineer a corresponding modified gravity model of the chameleon type. This
opens up the possibility of having independent constraints on modified gravity
from the CMB peaks and large scale structures at low redshifts.
