Dark matter as an effect of a minimal length

Abstract

In this work, we consider the implications of a phenomenological model of quantum gravitational effects related to a minimal length, implemented via the generalized uncertainty principle. Such effects are applied to the Bekenstein–Hawking entropy to derive a modified law of gravity through Verlinde’s conjecture. Implications on galactic scales, and in particular on the shape of rotational curves, are investigated, exploring the possibility to mimic dark matter-like effects via a minimal length.