Constraining f(R) gravity with cross-correlation of galaxies and cosmic microwave background lensing

Abstract

We look for signatures of the Hu-Sawicki modified gravity theory proposed to explain the observed accelerated expansion of the Universe in observations of the galaxy distribution, the cosmic microwave background (CMB), and gravitational lensing of the CMB. We study constraints obtained using observations of only the CMB primary anisotropies before adding the galaxy power spectrum and its cross-correlation with CMB lensing. We show that cross-correlation of the galaxy distribution with lensing measurements is crucial in order to break parameter degeneracies, placing tighter constraints on the model. In particular, we set a strong upper limit on $ at $95<!PCT!>$ confidence level. This means that while the model may explain the accelerated expansion, its impact on large-scale structure closely resembles general relativity (GR). This analysis is the first to make use of the galaxy clustering, CMB lensing, and their cross-correlation power spectra to constrain Hu-Sawicki gravity. Restricting the analysis to the linear regime, we place a robust constraint that is competitive with other cosmological studies whilst using fewer probes. This study can be seen as a precursor to cross-correlation analyses of gravity and can be repeated with next-stage surveys, which will benefit from lower noise and hence probe smaller potential deviations from GR.