  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.
