# Testing Verlinde's Emergent Gravity with the Radial Acceleration Relation

## TL;DR

This paper tests Verlinde's emergent gravity theory against the observed Radial Acceleration Relation in galaxies, finding it only consistent under certain assumptions and predicting residual correlations not observed.

## Contribution

It critically evaluates Verlinde's emergent gravity against empirical galactic data, highlighting discrepancies and limitations of the theory.

## Key findings

- EG aligns with RAR only with lower stellar mass-to-light ratios.
- EG predicts residual correlations with radius, not observed in data.
- Significant differences exist between EG and MOND in galaxy inner regions.

## Abstract

Verlinde (2016) has recently proposed that spacetime and gravity may emerge from an underlying microscopic theory. In a de Sitter spacetime, such emergent gravity (EG) contains an additional gravitational force due to dark energy, which may explain the mass discrepancies observed in galactic systems without the need of dark matter. For a point mass, EG is equivalent to Modified Newtonian Dynamics (MOND). We show that this equivalence does not hold for finite-size galaxies: there are significant differences between EG and MOND in the inner regions of galaxies. We confront theoretical predictions with the empirical Radial Acceleration Relation (RAR). We find that (i) EG is consistent with the observed RAR only if we substantially decrease the fiducial stellar mass-to-light ratios; the resulting values are in tension with other astronomical estimates; (ii) EG predicts that the residuals around the RAR should correlate with radius; such residual correlation is not observed.