CMB lensing bispectrum 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 bispectrum offer an interesting way to constrain deviations from GR in a broad class of scalartensor 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 bispectrum in the modified gravity considered is necessary when the bispectrum is used to probe scales beyond a multipole l(max) greater than or similar to 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 bispectrum 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.