Probing General Relativity in galactic scales at z $\sim0.3$

TL;DR

This study tests General Relativity at galactic scales by constraining the PPN parameter using combined gravitational lensing and stellar dynamics data for a galaxy at z~0.3, finding results consistent with GR predictions.

Contribution

First to combine lensing and stellar dynamics data with a flexible mass model to test the PPN parameter at galaxy scales, accounting for systematic uncertainties.

Findings

Measured η_PPN = 1.13 ± 0.03 (stat) ± 0.20 (sys)

Results are consistent with General Relativity predictions

Systematic uncertainties are dominated by kinematic data quality.

Abstract

General Relativity (GR) has been successfully tested mainly at Solar system scales; however, galaxy-scale tests have become popular in the last few decades. In this work, we investigate the $\eta_\text{PPN}$ parameter, which is commonly defined by the ratio of two scalar potentials that appears in the cosmological linearly perturbed metric. Under the assumption of GR and a vanish anisotropic stress tensor, $\eta_\text{PPN}= 1$. Using ALMA, HST, and VLT/MUSE data, we combine mass measurements, using gravitational lensing and galactic dynamics, for the SDP.81 lens galaxy ($z = 0.299$) to constrain $\eta_\text{PPN}$. By using a flexible and self-consistent mass profile, our fiducial model takes into account the contribution of the stellar mass and a dark matter halo to reconstruct the lensed galaxy and the spatially-resolved stellar kinematics. We infer, after accounting for systematic uncertainties related to the mass model, cosmology and kinematics, $\eta_{\text{PPN}} = 1.13^{+0.03}_{-0.03}\pm0.20\,(\text{sys})$, which is in accordance with GR predictions. Better spectroscopy data are needed to push the systematics down and bring the uncertainty to the percentage level since our analysis shows that the main source of the systematics is related to kinematics, which heavily depends on the signal-to-noise ratio of the spectra.