Raising galaxy rotation curves via dressing

TL;DR

The paper tackles the long-standing issue of galaxy rotation curves without invoking dark matter by applying the Dressing Field Method to a diffeomorphism-invariant GR system with a metric plus four scalar fields representing dust-like matter. The method yields a relational, gauge-invariant dressed metric and a velocity profile for circular orbits of the form $v^2 \approx \frac{GM}{\bar{r}} + v_0^2$, where $v_0^2$ is constant when the scalar dressing satisfies $\chi^r \propto \bar{r}^2$ and $\chi^r = k \bar{r}^2 /(1-2k\bar{r})$, with $v_0^2 = 3GM k$. Phenomenologically, fits to SPARC galaxies NGC 3198 and NGC 2403 yield excellent $R^2$ values (≈0.996) using a single free parameter $k$, reproducing flat rotation curves without dark matter. This work provides a gauge-invariant alternative viewpoint on galactic dynamics and lays the groundwork for extending the approach to cosmological perturbations and structure formation.

Abstract

We present a manifestly diffeomorphism-invariant simple model of galaxy dynamics obtained by applying the Dressing Field Method (DFM) to a general-relativistic system comprising the metric and four scalar fields, phenomenologically representing the four-velocity of a cosmological fluid or dust field. The DFM, a systematic tool for extracting the gauge-invariant content in general-relativistic theories, provides a physical coordinatization that yields corrective terms to the rotational velocity profile. These corrections produce galaxy rotation curves that combine a Keplerian and a constant velocity terms, effectively emulating a Dark Matter contribution. We compare DFM-derived rotation curves to observed data for spiral galaxies, from the Spitzer Photometry and Accurate Rotation Curves (SPARC) database, showing that the DFM allows to fit them well.

Figures (5)

• Figure 1: Rotation curves of NGC 3198 (a) and NGC 2403 (b). The black lines show observed velocities from the SPARC database Lelli:2016zqa. The red lines represent the DFM-derived rotation curve. The gray lines show the bare baryonic model prediction, assuming a Keplerian law.
• Figure 2: Observed rotational velocities of the galaxies NGC 3198 (a) and NGC 2403 (b). Data extracted from the SPARC database.
• Figure 3: Baryonic mass profile of the galaxies NGC 3198 (a) and NGC 2403 (b), derived by summing gas, disk, and bulge mass contributions.
• Figure 4: Comparison between the dressed model residuals (red points) and those of the bare baryonic model (gray points), for the galaxies NGC 3198 (a) and NGC 2403 (b).
• Figure 5: Other high-resolution rotation curves analyzed.