A new test of gravity -- II: Application of marked correlation functions to luminous red galaxy samples

TL;DR

This study applies a marked correlation function test to SDSS III luminous red galaxy samples to compare general relativity and $f(R)$ gravity, finding current data insufficient for discrimination but promising for future surveys.

Contribution

It demonstrates the application of the marked correlation function test to real galaxy data and assesses its potential to distinguish gravity models with improved future surveys.

Findings

Current galaxy catalogues are too small to distinguish $f(R)$ gravity from GR.

Uncertainty from halo occupation distribution models is comparable to sample variance.

Future surveys could enable the test to differentiate between gravity models.

Abstract

We apply the marked correlation function test proposed by Armijo et al. (Paper I) to samples of luminous red galaxies (LRGs) from the final data release of the Sloan Digital Sky Survey (SDSS) III. The test assigns a density-dependent mark to galaxies in the estimation of the projected marked correlation function. Two gravity models are compared: general relativity (GR) and $f(R)$ gravity. We build mock catalogues which, by construction, reproduce the measured galaxy number density and two-point correlation function of the LRG samples, using the halo occupation distribution model (HOD). A range of HOD models give acceptable fits to the observational constraints, and this uncertainty is fed through to the error in the predicted marked correlation functions. The uncertainty from the HOD modelling is comparable to the sample variance for the SDSS-III LRG samples. Our analysis shows that current galaxy catalogues are too small for the test to distinguish a popular $f(R)$ model from GR. However, upcoming surveys with a better measured galaxy number density and smaller errors on the two-point correlation function, or a better understanding of galaxy formation, may allow our method to distinguish between viable gravity models.