Using Global Gravitational Potential Weighted Correlation Function to Constrain Modified Gravity Models

Abstract

We propose a new marked two-point correlation function weighted by the global gravitational potential as a probe for testing gravity models. Using the LCDM model based on general relativity (GR) as a reference, we investigate two representative modified gravity (MG) scenarios: f(R) gravity and nDGP. The mark used in this work, the global gravitational potential that is reconstructed from the galaxy distribution via the Poisson equation, is in contrast to the local property based mark (e.g., local galaxy number density or gravitational potential of host halo) used in previous studies. By applying two weighting schemes to quantify environment-dependent clustering, we find that this statistic is able to distinguish MG models from GR, with the signal being enhanced in regions corresponding to particular ranges of gravitational potential. These results indicate that the proposed statistic can serve as a useful complement to conventional clustering probes in future surveys, once observational effects and modeling uncertainties are properly taken into account.

Figures (7)

• Figure 1: 2D slice of galaxy and potential distribution. The upper panel shows the slice of galaxy over-density field and the bottom panel shows the potential distribution calculated from Poisson equation. The results are from the first realization of GR model at $z=0.5$.
• Figure 2: Number of grids (upper panel) and galaxies (lower panel) with specified global gravitational potential values, which are estimated from the galaxy distribution. The result is from realization 1 in GR model at $z=0.5$. The negatively skewed peak in the lower panel is due to the fact that galaxies prefer to appear at high density and low potential region. The four dashed red lines in the bottom panel correspond to four potential thresholds used in step-function-type MCF in Section \ref{['StepFunc']}.
• Figure 3: Different forms of the MCF results for Sample 1 from the step-function-type marked galaxy correlation function. The upper panel shows $\mathcal{M}(r)$, the middle panel shows the signal-to-noise ratio (SNR), and the bottom panel shows the MCF fractional difference $\Delta M / M_{\mathrm{GR}}$. The error bars represent the standard error of mean over all 5 realizations. Error bars are plotted for every three data points to enhance graph clarity.
• Figure 4: The signal-to-noise ratio (SNR) and the MCF fractional difference $\Delta \mathcal{M} / \mathcal{M}_{\mathrm{GR}}$ of step-function-type marked galaxy correlation function at $z=0.5$ for GR and three $f(R)$ variants/two nDGP variants (left/right panels). Plots from upper to bottom correspond to varying potential threshold $\Psi_{\mathrm{thres}}$. The error bars of MCF fractional difference represent the standard error of mean over all 5 realizations.
• Figure 5: The signal-to-noise ratio (SNR) and the MCF fractional difference $\Delta \mathcal{M} / \mathcal{M}_{\mathrm{GR}}$ of rectangular-function-type marked correlation function of galaxy at $z=0.5$ for GR and three $f(R)$ variants/two nDGP variants (left/right panels). Plots from upper to bottom correspond to setting the weighting in each quartile as one and zero otherwise. The error bars of MCF fractional difference represent the standard error of mean over all 5 realizations.