Future CMB ISW-Lensing bispectrum constraints on modified gravity in the Parameterized Post-Friedmann formalism

TL;DR

This paper forecasts how well Planck satellite data can constrain modified gravity models using ISW-Lensing bispectrum and power spectrum analyses, showing significant improvements over previous constraints.

Contribution

It introduces a joint analysis method of ISW-Lensing bispectrum and power spectrum for constraining modified gravity within the PPF formalism, demonstrating improved parameter bounds.

Findings

Planck data can reduce errors on $B_0$ by at least an order of magnitude.

Joint bispectrum and power spectrum analysis improves constraints by a factor of 1.14 to 5.32.

Cross-correlation between bispectrum and power spectrum can be neglected in the analysis.

Abstract

We forecast the constraints on both Hu-Sawicki model and Bertschinger-Zukin model of modified gravity within the Parameterized Post-Friedmann (PPF) formalism for the Planck satellite experiment by performing the joint analysis of ISW-Lensing bispectrum and CMB power spectrum. We find that, even considering the temperature-temperature mode of CMB power spectrum only, Planck data are expected to reduce the error bars on the modified gravity parameter $B_0$ (related to the present value of Compton wavelength of the extra scalar degree of freedom) at least one order magnitude compared with WMAP. The spectrum-bispectrum joint analysis can further improve the results by a factor ranging from 1.14 to 5.32 depending on the specific modified gravity model. One of our main results is that the cross-correlation between ISW-Lensing bispectrum and power spectrum can be safely neglected when performing the joint analysis. For simplicity, we only investigate the likelihood of one parameter ({$B_0$}) and fix all other cosmological parameters to their best-fit values in WMAP7yr results.