The CMB lensing bi-spectrum as a probe of modified gravity theories
  Cosmological structures grow differently in theories of gravity which are
modified as compared to Einstein's General relativity (GR). Cosmic microwave
background (CMB) fluctuation patterns at the last scattering surface are lensed
by these structures along the photon path to the observer. The observed CMB
pattern therefore keeps trace of the growth history of structures. We show that
observations of the CMB lensing bi-spectrum offer an interesting way to
constrain deviations from GR in a broad class of scalar-tensor theories of
gravity called "beyond Horndeski". We quantify how the constraints on generic
parameters describing the deviations from GR depend on the effective multipole
range of the analysis. Our results further indicate that an accurate nonlinear
correction of the matter bi-spectrum in the modified gravity considered is
necessary when the bi-spectrum is used to probe scales beyond a multipole
$\ell_{\rm max} \gtrsim 1500$. We also found that the results are insensitive
to details of the implementation of the screening mechanism, at very small
scales. We finally demonstrate the potential of the lensing bi-spectrum to
provide a blind reconstruction of the redshift evolution of our modified
gravity parameters by combining the analysis of CMB and low-z source lensing
data.
