# Constraints on Chameleon f(R)-Gravity from Galaxy Rotation Curves of the SPARC Sample

## TL;DR

This study tests chameleon $f(R)$-gravity using galaxy rotation curves from the SPARC sample, finding no convincing evidence for $f(R)$ effects at current sensitivity levels and constraining the scalar field parameter $f_{R0}$.

## Contribution

It provides new constraints on $f(R)$-gravity from galaxy rotation curves, highlighting the degeneracy with core/cusp issues and comparing different halo profiles.

## Key findings

- Models with $oxed{ ext{log}_{10}|f_{R0}| > -6.1}$ are excluded.
- Favored $f(R)$ range is $-7.5< ext{log}_{10}|f_{R0}|<-6.5$, peaking at -7.
- No convincing evidence of $f(R)$ gravity at $|f_{R0}| o 6 imes 10^{-8}$.

## Abstract

In chameleon $f(R)$-gravity, the fifth force will lead to `upturns' in galaxy rotation curves near the screening radius. The location of the upturn depends on the cosmic background value of the scalar field $f_{R0}$, as well as the mass, size and environment of the galaxy. We search for this signature of modified gravity in the SPARC sample of measured rotation curves, using an MCMC technique to derive constraints on $f_{R0}$. Assuming NFW dark matter haloes and with $f_{R0}$ freely varying for each galaxy, most galaxies prefer $f(R)$ gravity to $\Lambda$CDM, but there is a large spread of inferred $f_{R0}$ values, inconsistent with a single global value. Requiring instead a consistent $f_{R0}$ value for the whole sample, models with $\log_{10}|f_{R0}| > -6.1$ are excluded. On the other hand, models in the range $-7.5<\log_{10}|f_{R0}|<-6.5$ seem to be favoured with respect to $\Lambda$CDM, with a significant peak at -7. However, this signal is largely a result of galaxies for which the $f(R)$ signal is degenerate with the core/cusp problem, and when the NFW profile is replaced with a cored halo profile, $\Lambda$CDM gives better fits than any given $f(R)$ model. Thus, we find no convincing evidence of $f(R)$ gravity down to the level of $|f_{R0}| \sim 6 \times 10^{-8}$, with the caveat that if cored halo density profiles cannot ultimately be explained within $\Lambda$CDM, a screened modified gravity theory could possibly provide an alternative solution for the core/cusp problem. However, the $f(R)$ models studied here fall short of achieving this.