The CMB lensing bi-spectrum as a probe of modified gravity theories

TL;DR

This paper explores how the CMB lensing bi-spectrum can be used to test and constrain deviations from General Relativity in scalar-tensor theories, emphasizing the importance of nonlinear corrections and the potential for redshift evolution reconstruction.

Contribution

It introduces the use of the CMB lensing bi-spectrum as a novel probe for modified gravity theories, especially beyond Horndeski, and analyzes the dependence on multipole range and nonlinear corrections.

Findings

Constraints depend on the multipole range of analysis.

Nonlinear matter bi-spectrum correction is necessary beyond $\, ext{l}_ ext{max} \,\gtrsim 1500$.

Results are insensitive to screening mechanism details at small scales.

Abstract

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.