# Reconstructing a Model for Gravity at Large Distances from Dark Matter Density Profiles

## TL;DR

This paper reconstructs an effective gravity model at large distances using dark matter density profiles, leading to a modified metric that better fits galaxy rotation curves and has potential cosmological implications.

## Contribution

It introduces a new effective gravity model derived from dark matter profiles, incorporating a Rindler acceleration term that improves galaxy rotation curve fits.

## Key findings

- The reconstructed model fits galaxy rotation data better than previous models.
- The new metric includes a Rindler-like acceleration term without singularities.
- Possible implications for cosmology are discussed.

## Abstract

Using the Navarro-Frenk-White (NFW) dark matter density profile we reconstruct an effective field theory model for gravity at large distances from a central object by demanding that the vacuum solution has the same gravitational properties as the NFW density profile has in the context of General Relativity (GR). The dimensionally reduced reconstructed action for gravity leads to a vacuum metric that includes a modified Rindler acceleration term in addition to the Schwarzschild and cosmological constant terms. The new term is free from infrared curvature singularities and leads to a much better fit of observed galaxy velocity rotation curves than the corresponding simple Rindler term of the Grumiller metric, at the expense of one additional parameter. When the new parameter is set to zero the new metric term reduces to a Rindler constant acceleration term. We use galactic velocity rotation data to find the best fit values of the parameters of the reconstructed geometric potential and discuss possible cosmological implications.